Abstract: A class of singular control problems is made nonsingular by the addition of an integral quadratic functional of the control to the cost functional; a parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsilon > 0</tex> multiplies this added functional. The resulting nonsingular problem is solved for a monotonically decreasing sequence <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{\epsilon; \epsilon_{1} > \epsilon_{2} > ... > \epsilon_{k} > 0\}</tex> . As <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k \rightarrow \infty</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsilon_{k} \rightarrow 0</tex> the solution of the modified problem tends to the solution of the original singular problem. A variant of the method which does not require that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsilon \rightarrow 0</tex> is also presented. Four illustrative numerical examples are described.