This is a very common problem, and basic trouble-shooting, as described above, is the way to go.
Some additional ideas:
1) is it a hum or a whine? A hum suggests a 60 Hz problem, a whine suggests something a tad higher in the spectrum. Hum is magnetically coupled, whine is electrically coupled. Shields do nothing to reduce magnetic coupling, but a good twisted pair does. Shields do a lot to reduce RF interference. So you have to identify the problem.
2) There is a lot of chatter about ground loops. For the most part you need to forget about ground loops, they are not the problem, and in fact they make life safer. Instead think in terms of victim and aggressor. Once you have determined if the interference is power line or RF you can start looking for victims (the loudspeakers) and aggressors (maybe the monitors, maybe other noise impressed on either the audio or power lines.)
3) When these loudspeakers were originally released I believe they suffered from the dreaded "Pin 1" problem - that is, the shield was connected to the inside of the cabinet. I also believe that Yamaha resolved the problem. So depending on how old your loudspeakers are you may want to look into "Pin 1" problems.
That, and Bit's description above ought to get you started. Come back with more info and we'll figure this out!