We discuss an a posteriori error estimate for collocation methods applied
to boundary value problems in ordinary differential equations with a
singularity of the first kind. As an extension of previous results
we show the asymptotical correctness of our error estimate for
the most general class of singular problems where the coefficient matrix
is allowed to have eigenvalues with positive real parts. This requires
a new representation of the global error for the numerical solution
obtained by piecewise polynomial collocation when applied to our problem
class.