The initial-value technique that was originally developed for solving singularly-perturbed nonturning-point problems (Ref. 1) is used here to solve singularly-perturbed turning-point problems exhibiting twin boundary layers. In this method, the required approximate solution is obtained by combining solutions of the reduced problem, an initial-value problem, and a terminal-value problem. Error estimates for approximate solutions are obtained. The implementation of the method on parallel architectures is discussed. Numerical examples are presented to illustrate the present technique.