Myosin Ⅴ and myosin Ⅵ are two classes of two-headed molecular motors of the myosin superfamily that move processively along helical actin filaments in opposite directions. Here we present a hand-over-hand model for their processive movements. In the model, the moving direction of a dimeric molecular motor is automatically determined by the relative orientation between its two heads at free state and its head's binding orientation on track filament.This determines that myosin Ⅴ moves toward the barbed end and myosin Ⅵ moves toward the pointed end of actin.During the moving period in one step, one head remains bound to actin for myosin Ⅴ whereas two heads are detached for myosin Ⅵ: the moving manner is determined by the length of neck domain. This naturally explains the similar dynamic behaviours but opposite moving directions of myosin Ⅵ and mutant myosin Ⅴ (the neck of which is truncated to only one-sixth of the native length). Because of different moving manners, myosin Ⅵ and mutant myosin Ⅴ exhibit significantly broader step-size distribution than native myosin Ⅴ. However, all the three motors give the same mean step size of ~36nm (the pseudo-repeat of actin helix). All these theoretical results are in agreement with previous experimental ones.