Hi Charles, I have performed an experiment of an oscillator that oscillates at more than one frequencies simultaneously, using a single active device.
I have written everything in my page here http://qrp.gr/multiosc/
Do you have any idea why this circuit worked for me, whereas others tested it and said it did not work?
Are you aware of any other such circuits, or am I the first one to try such a thing?

The problem with others' circuits is probably crystal activity differences. The limiting caused by the "stronger" crystal will kill the gain sufficiently that the others don't start. I'd recommend that the experimenter observe which crystal is oscillating and then add series resistance to kill it's activity a bit, on the order of 10's of ohms. Another crystal should come alive and eventually series resistors in the right crystal legs should allow for fairly equal outputs.
We actually have to fight the phenomenon when using SC-cut crystals that have a strong activity only 10% above the desired mode.

Did I achieve the same result you mention (gain killing resistors, for equal outputs) when I added the series capacitors to the crystals instead of the resistors you mention?
I used cheap (probably AT-cut) crystals for all frequencies.

The capacitor is reactive and will raise the frequency. It's a secondary effect that it drops the Q a bit.