It is shown that resonant triads exist for Kelvin–Helmholtz waves. The loci of various triad modes in wavenumber space are discussed in detail. In most cases of interest one of the three triad modes lies very close to the Kelvin–Helmholtz cutoff wavenumber and hence direct resonance occurs. Evolution equations are first derived in wavenumber space and then transformed into physical space. Interactions among various triad modes occur on a much faster time scale and the amplitudes of various modes are much larger than the amplitudes for a regular triad. The stability of a plane wavetrain subject to perturbations from resonant triad modes is examined.