The Quasi-Steady-State Approximation (QSSA) is a method of getting approximate solutions to differential equations, developed heuristically in biochemistry early this century. It can produce acceptable and important results even when formal analytic and numerical procedures fail. It has become associated with singular perturbation theory [1], which provides a means of assessing the accuracy and validity of the QSSA, but this involves rather complicated mathematics. In contrast, it is shown here how the necessary safeguards against misuse can be based on a simpler intuitive approach to singular perturbation theory, allied to the powerful numerical mathematical packages which have become available in recent years. This approach has been subjected to rigorous analysis and has been applied to problems in transport theory and chemical kinetics. In this note, examples are restricted to the case of ordinary differential equation systems involving only a few dependent variables. Use of the QSSA is described ab initio.