Summary: A higher order Runge-Kutta (pair) method specially adapted to the numerical integration of IVPs with oscillatory solutions is presented. This method is based on the adapted methods proposed by J.M. Franco
[Appl. Numer. Math. 50, No. 3-4, 427–443 (2004; Zbl 1057.65043
)]). We give explicit method (up to order 5) as well as pairs of embedded Runge-Kutta methods of order 5 and 4 designed using the FSAL properties. The stability of the new methods is analyzed. The numerical experiments are carried out to show the efficiency and robustness of our methods in comparison with some efficient methods.