We show that nonreciprocal optical Bloch-like oscillations can emerge in transversely magnetized waveguide arrays in the presence of an effective index step between the waveguides. Normal modes of the system are shown to acquire different wavenumbers in opposite propagation directions. Significant differences in phase coherence and decoherence between these normal modes are presented and discussed. Nonreciprocity is established by imposing unequal vertical refractive index gradients at the substrate/core and core/cover interfaces in the presence of transverse magnetization.