Some time ago, I built a small test rig to draw Ia-Vg curves for valves which could then be used as standards for a valve tester. The first time I put in an ECC81 (with just one side hooked up), it started oscillating with no help at all from me. I had to go to some trouble to stop it; lots of ferrite beads on the leads etc.
I think it's Tanuki who occasionally points out that every amplifier aspires to be an oscillator. I think you can add to that that once a valve finds out it can oscillate, it prefers to do that rather than just amplify
.
B