General LINEAR METHODS (GLMS) WERE INTRODUCED AS THE NATURAL GeneralIZATIONS OF THE CLASSICAL RUNGEKUTTA AND LINEAR MULTISTEP METHODS. AN EXTENSION OF GLMS, SO-CALLED SGLMS (GLM WITH SECOND DERIVATIVE), WAS INTRODUCED TO THE CASE IN WHICH SECOND DERIVATIVES, AS WELL AS FIRST DERIVATIVES, CAN BE CALCULATED. IN THIS PAPER, WE INTRODUCE THE BASIC CONCEPTS, CONSTRUCTION AND IMPLEMENTATION OF SGLMS.