A hand-over-hand model is presented for the processive movement of two-headed kinesin based on previous structural and biochemical studies. In the model, the ATPase activities of the two heads are regulated by forces, both from internal elasticity and external load, exerted on their neck linkers. The results from the model show that the two heads may be partially coordinated in their ATPase cycles: in the case of backward load or low forward load, the ATPase cycles of its two heads are well coordinated, whereas in the case of high forward load, they are no longer well coordinated. The model gives results that show good quantitative agreement with both previous biochemical and mechanical experimental results such as the limping of homodimers and the dependences of mean velocity on [ATP] and on loads (both positive and negative). Furthermore, using the model we study the kinetics of a number of mutant kinesin homodimers and heterodimers, showing that the two heads' ATPase activities of some of these molecules are not well coordinated and they move processively with low mechanochemical coupling efficiencies even under no load. The theoretical results of ATPase rate per head, moving velocity, and stall force of the motors show good quantitative agreement with the experimental ones. The puzzling dynamic behaviours of mutant homodimeric and heterodimeric kinesins become understandable.