The two tone intermodulation distortion arising in MgB2 thin films synthesized by hybrid physical-chemical vapour deposition is studied in order to probe the influence of the two bands on the nonlinear response of this superconductor. The measurements are carried out by using a dielectrically loaded copper cavity operating at 7 GHz. Microwave data on samples having critical temperatures above 41 K, very low resistivity values, and residual resistivity ratio larger than 10, are shown. The dependence of the nonlinear surface losses and of the third order intermodulation products on the power feeding the cavity and on the temperature is analyzed. At low power, the signal arising from distortion versus temperature shows the intrinsic s-wave behavior expected for this compound. Data are compared with measurements performed on Nb and YBCO thin films using the same technique.