will my electrical appliance work in Italy, France and Spain?

The Hz are unimportant unless there is a timing element built in. As along as your input says something about 120-240, 250v you are good to go. You will need the appropriate plug adapter to plug into the outlet. If it is something like a hair dryer or curler or iron it may not perform very well but it will not melt down.

What's the brand and model name of the appliance? Without knowing what it is I would generally say no and you should buy one over there. Usually electronics are the things that work fine overseas. They clearly say 100-240v 50-60hz on the power adaptor.

Read:
https://www.ricksteves.com/travel-tips/phones-tech/electric-adapters-converters

The spec seems odd. The 125v is on the high side with 110 or 120 usually the north american voltage and the 250v being in the high side. Also odd that it's only spec'd for 60 Hz and not also 50Hz. If it is or has a clock device it will run slow with 50 Hz Euro power.

ksb,

It would help to have some information on exactly what type of "travel appliance" you're referring to? I'm somewhat puzzled at the "60 Hz" specification they listed, as if the product is designed for 250 VAC then it should also be able to operate on 50 Hz. If this product was manufactured in one of the off-shore countries, their labelling standards may be a bit lax.

You will of course need a Plug Adaptor to connect the appliance in Europe.

Calling it an electrical appliance, or "travel appliance" is a bit unusual - they tend to be big and with a motor.

More specific would help a lot. The frequency (Hz, means cycles per second) it is expecting - whatever it is - will make a difference if it has a motor or timer.

I agree that 125/250 is higher than most commercial supplies around the world.

Ksb, any chance you're reading the plug, rather than the manufacturer's "nameplate" on the device itself? Why did you write "electrical appliance" in your OP? No one talks that way. Is it a medical device? We don't have any actual interest in your medical condition, but that would make the quality of the answer a matter a life and death.

If it is or has a clock device it will run slow with 50 Hz Euro
power.

To be totally honest I don't thing anyone traveling in 2015 will use an electronic device that still uses synchronous clocks (i.e. frequency counting) as its method of timing. Quartz clocks have replaced those fairly thoroughly since the 80s...

I agree with others, it would be helpful to know exactly what the device is, but I would normally expect it to work. Few devices today depend on the frequency to work. I had an electric razor in 1987 that had a voltage switch for "220V", but ran slow on 50 Hz and felt like it was pulling the hairs out.

BTW, 125V is not so unusual. I just measured the voltage at my house and it was 121.5V, and I'm nowhere near the power generating station. And, 250V is, or was, the standard voltage in western Australia (Perth). I know because a company I worked for sold our product made for 220V in Europe to western Australia, and the motors burned up.

Clock speed of a synchronous AC motor is proportionate to the line frequency. If the appliance's motor is designed for 60 Hz it will run slow (5/6 the usual speed) if powered by the 50 Hz common to European power.

The lower specified voltage limit of 125v would be a problem in countries where standard residential voltage 110v and during US high demand "brownout" conditions. Under voltage is defined as being 10% low. Under voltage conditions can strain motors as torque drops.

Thank you to all who sought to offer helpful advice in answering my question. (Tim; criticizing my choice of words.... i.e. "No one talks that way".....and suggesting that I was not reading the proper part of the appliance was not helpful).

Indeed if I could post a picture of the description written on the handle of the appliance, I would do so, for those who doubt that the numbers I gave were correct.

Also, I purposely did not say what kind of appliance I wanted to take with me, because I had read other threads on this forum where people asking questions about their own similar appliance were told to just buy a new one there. That also is not really a helpful answer, since purchasing a new one would take excess time, money, and trial and error to get one that worked for my needs. This is why I did not state what the appliance is.
I have two of these appliances and both list the voltage as 125/250 (so apparently it is not all that uncommon). One does list the Hz as 50/60 but I didn't want to take that one, since it is heavier. The appliance about which I asked, was described as specifically being manufactured for "travel". It was manufactured in China, and maybe that qualifies as an "off shore" country.
Again, thank you for those who sought to provide me with useful information.

Judging from the answers I received, it appears my best choice would be to take the heavier one which states it is for 125/250 VAC and 50/60 Hz. thank you

Well, ksb, you'll never know whether my electrical experience would have been helpful to you, or not, will you? If you found it discourteous, I'm actually, truly sorry. When someone spoils the chance to get good advice, they should be warned what they are doing.

As you revealed, you were deliberately obscure. And at least one poster agreed with me. Today, you cannot get a UL listing on a product with a rating with a slash in it. That's why Apple wall-warts (just for example) say 100-250, or something like that. I am not surprised to hear that the device was made in China. Good luck on your trip.

Just as I suspected, the product was manufactured off shore which explains the shoddy labelling. That doesn't meet UL/CSA labelling requirements so I'm surprised they're allowed to import them.

Many of the newer electronic devices such as iPhones, iPads, etc. almost always state Input 100-240 VAC, 50~60 Hz, so I'm surprised they didn't use a similar format for your device. I suspect the lighter of the two products is designed for operation on 50 Hz electrical systems, but the idiots that labelled it failed to include that information.

As you're not willing to divulge the nature of the product, it's difficult to provide much more specific information.

If they are that poor with the labeling, I worry about the electrical integrity of whatever it is. I especially would not want to rely on any purported double insulation (indicated on a label - if they bothered - by a small square box inside a small square box) which protects you from electric shocks if the device is not earthed/grounded. If you only have 2 prongs on the plug it should have that symbol, but if it is counterfeit or otherwise cheaply made the symbol may be meaningless.

ksb, I know you feel persecuted by it appearing that people are not directly answering your questions. Just understand that a number of us here have some engineering and electronic/electrical background - I myself used to test electronics and electrical equipment for the US Navy - and we have some idea of potential hazards. I myself have survived a high voltage shock but I didn't think I would.

I would be very chary of anything that would come into contact with me that had not bothered to dot the i's and cross the t's on an electrical label.

You do what you want - I just want you to know the risks.

Nigel makes a good point about the double-insulated devices (square in a square symbol). Any device with a two prong plug (ungrounded) should be double insulated. Further, the two pin (Europlug) plug is only for devices drawing less than 2½ amps (575 Watts on 230V). If you put any device drawing more than 2½ amps (a hair dryer) on a Europlug, you are not in compliance with the codes.

Further, many American devices have a polarized plug (one blade wide than the other. You've seen them.) These devices depend on the polarize receptacle (one side at neutral potential) for safety. But almost no European receptacles are polarized, so the safety that depends on the polarized plug could be lost. (Swiss plugs are polarized, but if you use a non-grounding, 2-pin adapter, you can plug it in either way, so 50% of the time the safety is lost.) Do not take to Europe any device with a polarized plug.

In reality, you should not take to Europe any device that does not show the "CE" mark.