The paper derives sharp local error estimates for a defect-correction method applied to the one-dimensional model problem \(-\epsilon u''+f(x)u'+g(x)u=q(x),\) \(0<x<1\), \(f>0\), \(u(0)=\alpha\), \(u(1)=\beta\). The kth approximation is shown to converge uniformly in \(\epsilon\) in regions bounded away from the layer with rate \(O((\epsilon_ 0-\epsilon)^ k+h^ 2)\), \(\epsilon_ 0=O(h)\) while near the layers the estimate degrades to O(1). These theoretical estimates are supported by a numerical example.