The generalizedα method and αRATTLE method were used in the numerical integration of nonholonomic constrained mechanical systems,i.e. numerical solution of index2 DAEs directly.During the integration,these two α methods can settle the systems that their mass matrices are related with generalized coordinates. Finally,the two methods were verified by a numerical example,the classical nonholonomic constrained mechanical system: Snakeboard. The results were compared with those obtained by the solver DASSL.