  We extend our studies of microwave photoresistance of ultra-high mobility
two-dimensional electron system (2DES) into the high-intensity, non-linear
regime employing both monochromatic and bichromatic radiation. Under
high-intensity monochromatic radiation $\omega$ we observe new zero-resistance
states (ZRS) which correspond to rational values of $\epsilon=\omega/\omega_C$
($\omega_C$ is the cyclotron frequency) and can be associated with multiphoton
processes. %Formation of these rational ZRS is accompanied by a dramatic
reconstruction of the photoresistance spectrum which reveals diminishing,
narrowing, and phase reduction of the resistance peaks, as well as overall
suppression of resistance at $\epsilon<1/2$. Under bichromatic radiation
$\omega_1,\omega_2$ we discover new resistance minimum, possibly a precursor of
bichromatic ZRS, which seems to originate from a frequency mixing process,
$\omega_1+\omega_2$. These findings indicate that multiphoton processes play
important roles in the physics of non-equilibrium transport of microwave-driven
2DES, and suggest new directions for theoretical and experimental studies.
