The sound of electrolytic capacitors failing

My system (all 20-30 year old high end gear) has started to have a sound problem. I'm hearing some breakup on peaks and a few Db shift to the right side in balance for the first hour or two of playing. At some point after that, everything suddenly snaps into a proper sound, usually in the middle of a song. I know the problem is either in my preamp or amp. Could it be one of the power supply caps breaking down? Any other ideas?
Swap the L&R to the amp. If the problem switches, it's your pre.

It could be a lot of things. At 20 years, replacing PS caps is a good idea.
That was a great suggestion,Thanks!
It’s in my amp, the power supply caps are US$190 per side. :-(

Have your amp checked out soon. $190 is a lot, but not as much as having a bad cap take out all the power transistors, or a speaker. :)

@erik_squires A bad filter capacitor won't take out power transistors but it should damage the power *transformer*.
One question that remains unanswered: What changes in the sound when a power cap is failing? 
Depending on the severity of the failure it can manifest in several ways
Increased hum
less bandwidth extension in either direction (this is due to the audio circuit interacting with power supply components that it normally would not) and less detail
'motorboating', a repetitive thumping sound, which may or may not vary with the volume and other controls. This problem usually occurs when more gain is present.

Sometimes the filter cap 'opens up' which is to say that its capacitance dwindles to nothing. In other cases the capacitor develops a significant lw resistance, which then draws power from the power supply (and can heat up the capacitor, which then will draw even more current). It is this failure mode which can destroy power transformers.
Thanks! I'm hearing distortion on high level transients, especially mid and high frequencies which disappears after about 1 hour of listening. I've been assuming it takes that long for the caps to recondition (or whatever the term is). Is there a way to measure if the caps are in spec?
I've been assuming it takes that long for the caps to recondition (or whatever the term is). Is there a way to measure if the caps are in spec?
'Form up' is the technical phrase, and yes. They would have to be measured when cold and discharged to see how much current they need to charge up and what value they actually are. This does sound like a cap failure though.

I'm working on an amp right now that won't even play when you first turn it on- after about 30 seconds you can hear distortion, and after about two minutes its sounding about right. Both channels- so it can only be the power supply. I suspect a cap and probably the resistor the feeds it as well.

But one thing about trouble-shooting: never make assumptions!