We present theoretical investigations of meandering dynamics on vicinal surfaces during MBE growth. Our results are based on the numerical simulation of a step flow model, which accounts for asymmetric attachment/detachment kinetics at the steps. In the long wave regime, where the meander wavelength is large compared to the terrace width, our simulations of the full model confirm the results of Pierre-Louis et al. [Phys. Rev. Lett. 80 (1998) 4221; Phys. Rev. E 68 (2003) 020601; J. Crystal Growth 275 (2005) 56], based on a local amplitude equation: we observe meandering with a wavelength being determined by the linear instability in the early stage, and endless growth of the amplitude; in the presence of anisotropic edge energy, interrupted coarsening does take place. When passing to shorter wavelengths we reveal two other types of nonlinear dynamics: (a) mushroom formation and subsequent pinch-off leading to a vacancy island, and (b) emerging of a stationary step profile with fixed amplitude. (C) 2006 Elsevier B.V. All rights reserved.