If a neighbour reports television interference on one or two channels only when you transmit on 15 metres, what is probably the cause of the interference?

When interference appears on only one or two specific television channels rather than across the whole spectrum, it is typically caused by a specific frequency mapping to those channels. The 15-meter amateur band (21 MHz) has harmonics (like the 3rd harmonic at 63 MHz) that fall directly into the lower VHF television channels (like Channel 3 at 60-66 MHz). Receiver front-end overload would affect all or most channels simultaneously, not just one or two. Splatter or parasitic oscillations would also cause broader, more localized interference rather than landing cleanly on specific TV channels. Therefore, harmonic emissions are the primary suspect.