We show numerically that a single mode laser that is frequency modulat
ed for resonance at the line centre exhibits extremely weak small sign
al response compared to off-resonance cases where modulation frequenci
es are integer fractions of the line centre relaxation oscillation fre
quency. In fact in some cases the response rises by as much as two ord
ers of magnitude. Thus an instability is indicated here for the first
time with realistic values of the modulation index.