  We calculate the intrinsic nonlinear microwave response of the two gap
superconductor MgB2 in the clean and dirty limits. Due to the small value of
the pi band gap, the nonlinear response at low temperatures is larger than for
a single gap Bardeen-Cooper-Schrieffer (BCS) s-wave superconductor with a
transition temperature of 40 K. Comparing this result with the intrinsic
nonlinear d-wave response of YBa2Cu3O7 (YBCO) we find a comparable response at
temperatures around 20 K. Due to its two gap nature, impurity scattering in
MgB2 can be used to reduce the nonlinear response if the scattering rate in the
pi band is made larger than the one in the sigma band.
