In the singular perturbation theory, the solution of ODEs may be approximated by DAEs. For coarse tolerances, the computation time for a numerical solution may be decreased significantly due to the quasistatic approximation. Under certain conditions, the approximation error is bounded independent of the length of the time interval. Supersingularly perturbed problems are also considered. Decoupled equations of motions with small masses or large stiffness terms are analyzed by means of the singular perturbation theory. The Schur reduction is invented to formulate DAEs without diagonalizing the inertia matrix. Furthermore, the quasistatic approximation of equations for constrained systems is constructed. The computational savings of the proposed quasistatic approximation are illustrated e.g. by a flexible four bar mechanism.