They operate normally into a dummy
load. The problems start when connected to an antenna. At low output levels,
there are multiple frequencies present. It's not just harmonics.

Chris-

I agree with Allison that you should look at the power bus. You often find
designs with two or three parallel filter capacitors with values spread over
the range of 100 pf to 10 uf, all with shortest possible leads including PCB
tracks. As I recall, this was part of the cure for oscillations in the
Heathkit 10W Walkie-Talkie amplifier.

Then there is the effect of load impedance (or input impedance on the previous
stage) and its relationship to a VSWR protection circuit. With a resistive
load, even out-of-band signals are matched, so there is no drive reduction.
Therefore you have full power which seems to prevent the other-frequency
oscillation from occurring. However, a real-world antenna may be matched at
the intended frequency, but not at out-of-band frequencies. The VSWR
protection circuit reduces drive, which allows the spurious oscillation to
grow, causing more out-of-band signal, reducing drive even further. The result
is a complex waveform consisting of intermodulation products of the intended
signal and the spurious signal(s). This effect would be more likely to occur
where drive reduction is accomplished before the stage that is oscillating.

Although not a cure, you might try defeating any VSWR protection circuit in
either the driver or the amplifier, and see if the problem is reduced.

I found an almost identical problem in the old Regency HR-6 and BTL-301
tranceivers. The only thing that actually seemed to cure the problem was to
short the emitter lead of the final multiplier stage to ground. I noticed that
later versions of the BTL-301 moved the VSWR protection drive reduction from an
early stage to a later stage. This made significant improvement, but wasn't a
perfect cure.

73, Fred, K4DII