We discuss an a-posteriori error estimate for the numerical
solution of boundary value problems for nonlinear systems of
ordinary differential equations with a singularity of the first
kind. The estimate for the global error of an approximation
obtained by collocation with piecewise polynomial functions is
based on the defect correction principle. We prove that for
collocation methods based on an even number of equidistant
collocation nodes, the error estimate is asymptotically correct.
As an essential prerequisite we derive convergence results for
collocation methods applied to nonlinear singular problems.