About a decade ago Brownian motors were introduced as a possible mechanism for motor protein mobility. Since then many theoretical and experimental papers have been published on the topic. While some experiments support Brownian motor mechanisms, others are more consistent with traditional power stroke models. Taking into account recent experimental data and molecular level simulations, we have developed a stochastic model which incorporates both power stroke and Brownian motor mechanisms. Depending on parameter values, this motor works as a power stroker, a Brownian motor or a hybrid of the two. Using this model we investigate the motility of single-head myosins, two-head myosins and a group of myosins (muscle). The results are compared with some experimental data.