  The computational singular perturbation (CSP) method is an algorithm which
iteratively approximates slow manifolds and fast fibers in multiple-timescale
dynamical systems. Since its inception due to Lam and Goussis, the convergence
of the CSP method has been explored in depth; however, rigorous applications
have been confined to the standard framework, where the separation between
`slow' and `fast' variables is made explicit in the dynamical system. This
paper adapts the CSP method to {\it nonstandard} slow-fast systems having a
normally hyperbolic attracting critical manifold. We give new formulas for the
CSP method in this more general context, and provide the first concrete
demonstrations of the method on genuinely nonstandard examples.
