I have not had sibilance on this amp. Your scope output looks clean and devoid of excessive ringing. But should not burn resistors - those are meant to stop oscillation. You may have oscillation at MHz frequency? Try increasing the small pF compensation caps little by little. Add 5 to 10pF more value. Use silver mica caps if possible.
The oscillation could very well be up in UHF or maybe just VHF. A 100 MHz DSO is not the right instrument to sort that out. You have access to an analog scope? No, try a detector. Reverse the positions of the zobel network. (Put C first, then R). Feed the junction into a full wave bridge rectifier made out of 1N4148’s. Put a .01 uF cap across the +/- outputs, and feed into a DC meter. If you get a detected DC, it IS oscillating.
Thanks guys for the tips! Bandwidth drops to about 70 percent amplitude at 430kHz, and no (visible) oscillations during operation... White smoke came out of the 4.7 Ohm resistor only when powering up... Some schematics have a 10 Ohm resistor in that place ... What's the difference? I still have an old Telequipment oscilloscope, so I can connect that too, what should I pay attention to? XRK, when 100pF were installed in B-C, the siblings were quite pronounced, and when I removed them, the siblings decreased a lot, but they are still present... I did not write that in the input part, instead of 3503, an 1845 transistor was placed, and instead BD139 in quiescent current regulation circuit is 3503... Perhaps the cause is oscillations in the sensitivity of the amplifier, with a 1V input signal, the output signal has a value of 39V, so it has 39 times the amplification....