We demonstrate an efficient intracavity nonlinear interaction of laser modes in a specially adapted quantum cascade laser. A two-wavelength quantum cascade laser structure emitting at wavelengths of 7.1 and 9.5 micrometer included cascaded resonant optical intersubband transitions in an intracavity configuration leading to resonantly enhanced sum-frequency and second-harmonic generation at wavelengths of 4.1, 3.6, and 4.7 micrometer respectively. Laser peak optical powers of 60 and 80 mW resulted in 30 nW of sum-frequency signal and 10-15 nW of second-harmonic signal, both in good agreement with theoretical calculations.