J. Comp. Math., 13 (1995), pp. 232-242. High-Accuracy P-Stable Methods with Minimal Phase-Lag for y"=f(t,y) K. L. Xiang 11 Department of Basic Sciences, Southwest Petroleum Institute, Sichuan, China Abstract In this paper, we develop a one-parameter family of P-stable sixth-order and eighth-order two-step methods with minimal phase-lag errors for numerical integration of second order periodic initial value problems: y''=f(t,y), \quad y(t_0)=y_0, \quad y'(t_0)=y'_0. We determine the parameters so that the phase-lag (frequency distortion) of these methods are minimal. The resulting methods are P-stable methods with minimal phase-lag errors. The superiority of our present P-stable methods over the P-stable methods in [1--4] is given by comparative studying of the phase-lag errors and illustrated with numerical examples.