The nonlinear properties of quasiperiodic photonic crystals based on Thue-Morse sequence are investigated. The intrinsic asymmetry of these 1D structures for odd generation numbers results in bistability thresholds which are sensitive to propagation direction. Along with resonances of perfect transmission, this feature allows to obtain strongly nonreciprocal propagation and to create an all-optical diode (AOD). The efficiency of two schemes is compared: passive and active when an additional short-term pump signal is applied. The existence of stationary gap solitons for quasiperiodic photonic crystals is shown numerically, and their difference from the Bragg case is emphasized.