  In this paper, we will develop an iterative procedure to determine the
detailed asymptotic behaviour of solutions of a certain class of nonlinear
vector differential equations which approach a nonlinear sink as time tends to
infinity. This procedure is indifferent to resonance in the eigenvalues.
Moreover, we will address the writing of one component of a solution in terms
of the other in the case of a planar system. Examples will be given, notably
the Michaelis-Menten mechanism of enzyme kinetics.
