The nonlinear surface impedance and intermodulation distortion (IMD) products of MgB2 thin films have been measured as a function of power and temperature from 1.7 K to TC. Both dielectric and metallic substrates have been employed. The measurements on dielectrics use a stripline-resonator technique at 2 GHz. The measurements on metallic substrates have been carried out using a dielectric-resonator method at 10 GHz. The films were grown using the deposition technique of reactive evaporation onto LaAlO3, sapphire, and buffered copper, and stainless steel substrates. The low-power RS(T) is comparable to that of sputtered Nb films on sapphire, and lower than that of YBCO at the corresponding reduced temperatures. The rf-magnetic-field dependence at T< 20 K follows a moderate slope without breakdown for H< 500 Oe, the limit of the experiment. The measurements of IMD are compared with a theoretical analysis that assumes uncoupled π and σ channels and intrinsic nonlinearity to the lowest nonlinear order in the radiation field. While the temperature dependence of the measured IMD on dielectric substrates reflects the calculations qualitatively, it shows features that are not consistent with pure s-wave behavior.