This paper concerns families of constrained differential systems having the form {fx1-1} where h: a"e (n) -> a"e is a C (r) -function, (alpha (1), aEuro broken vertical bar, alpha (n) ) is a C (r) vector field on a"e (n) , r a parts per thousand yen 1, x a a"e (n) and lambda is a real parameter. Using singular perturbation techniques we present some results on the dynamics of the system around a point (x, lambda) of the impasse set lambda = h(x). In addition, planar constrained systems with non-regular impasse surfaces are considered.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)