A two-step nonlinear sequential reaction mechanism is studied as a dimensionless model of kinetic control. In this mechanism the unimolecular step is: A --> B, and the bimolecular step is: A + B --> C, with normalized initial conditions. For epsilon << 1, little C is formed, whereas for epsilon >> 1, the concentration of B approaches a steady state and C is the main product. Because of the coupling between the two reaction steps the steady-state approximation (SSA) is both a nullcline and a solution of the ordinary differential equations (ODEs) for the model. All concentrations can be expressed in terms of a timelike, real phase variable phi, whose evolution is described by a first-order, nonlinear ODE. Algorithms for the systematic perturbation solution of this ODE for large and small e are given.