For racing motorcycles used in MotoGP class need to have strong acceleration performance without accompanying abrupt behaviors for achieving faster running. This paper describes two control systems for engine torque used for MotoGP applying physical models which represent vehicle behaviors. One of these models is to describe wheelie which is the phenomenon of lift-ups of the front wheel caused when the vehicle is accelerated. This model includes dynamic effects of several inertial forces. The acceleration limit, restricted by avoiding wheelie occurrence, was calculated through the model. On the other hand, another model was constructed with the model using the estimation results of tire friction coefficients which were to be multiplied by the estimated values of normal forces at contacting point to the ground. Tire friction coefficient curve was derived from the distribution of the actual measured data based on tire friction ellipse. Normal force was designed taking account of the effect of the force applied on the chain. The traction limit was calculated through the model based on the restrictions from the tire grip. The calculated limits were converted into the values of torque applied on the crankshaft taking the drags and the inertial torques of rotating parts into consideration. It was demonstrated that these two control systems successfully controlled the engine torque just under the calculated limits while avoiding abrupt vehicle behaviors.