The frozen-magnon approach is employed to calculate the exchange parameters and critical temperatures of α and β MnAs. The data obtained are used to interpret the properties of the sequence of phase transitions in the material. It is found that the system, despite well-defined Mn moments, cannot be quantitatively described within the Heisenberg model. This conclusion is related to the properties of induced As moments. An unusual nonmonotonous dependence of the induced As moments on the net magnetization of the Mn sublattice is obtained. It is shown that such a behavior can be the reason for the canting of the Mn moments.