On Mon, 15 Mar 2010 17:17:14 -0400, mm
wrote:

I have an clock radio about 30 years old that, when tuning for 88.5
FM, for example, by turning the dial, will find that station, and then
a little higher will be another station, and a little higher still
will be 88.5 again, often a stronger signal than the first one.

I'm sure it's not a second station playing the same stuff.

I know about harmonics on AM MW and Short Wave, but here the tuned
frequencies are so close, and also I didn't think there was stuff like
this involving FM. What is going on?

It's poor filtering that allows an image of the desired signal. That
image is the intermediate frequency away from the ordinal.