You don't mention what the gear is, but if it includes a motor driven by line voltage (e.g. a turntable) you're probably out of luck. The motor would require 50Hz line frequency vs. the 60Hz used here. For most equipment, a transformer-based converter should do the trick. Just make sure that the power rating for the transformer is sufficient. These are not the "small, cheap" ones you refer to but can be had starting around $30. If the equipment requires considerable power (e.g. a power amp), you should look into having professionally rewired for 120V US power. Be aware that rewirng the power transformer will likely void the warranty however (unless the factory can accomodate you).

Also your current transformer inside your equipment might have the ability to be wired for either voltage. Cheaper for the manufacturer to make only one configuration.
Not always obvious though.

Many years ago,i bought a Pioneer Elite CLD-99 Laserdisc player from the states,brought it here,went to a electronics
store and bought a mains step-up converter (a cheap RS one)
and it works perfectetly even now.I don't see why the opposite would be a problem,a European dvd with a step-down
transformer.

Quote:
And since the player is designed for 50Hz, I don't know if this is an issue. I know it doesn't use the cycles for timing, but i don't know enough to say that it has no other effect on the player.

You're correct that line frequency is not used for timing in your player - and the motor that spins the disk receives DC from control circuitry. It is very unlikely that you will encounter any difficulties or experience any degradation of performance using a 1:2 step-up transformer.

Sometimes, but not very often in this day and age, AC line transformers made for 60Hz and run on 50Hz could overheat, though probably most nowadays are made to be both in this global shipping economy. In australia, do motors run backwards if made for the upper hemishpere? Don't their toilets flush backwards?