In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero. More precisely, the solution cannot be uniformly approximated by an asymptotic expansion as.

Singular perturbation theory concerns the study of problems featuring a parameter for which the solutions of the problem at a limiting value of the parameter are different in character from the limit of the solutions of the general problem; namely, the limit is singular.

Differential problems in which a small parameter, often referred to as a perturbation parameter, multiply the highest derivatives are called singularly perturbed differential problems.