  We explore experimentally bichromatic (frequencies $\omega_1$ and $\omega
_2$) photoresistance of a two-dimensional electron system in the regimes of
microwave-induced resistance oscillations and zero-resistance states. We find
bichromatic resistance to be well described by a superposition of $\omega_1$
and $\omega_2$ components, provided that both monochromatic resistances are
positive. This relation holds even when the oscillation amplitudes are small
and one could expect additive contributions from monochromatic
photoresistances. In contrast, whenever a zero-resistance state is formed by
one of the frequencies, such superposition relation breaks down and the
bichromatic resistance is strongly suppressed.
