Numerical methods having the property of preserving an asymptotic solution of a system of ordinary differential equations are regular methods. This paper considers the conditions that guarantee regularity and strong regularity properties of a general linear method to derive a family of variable order strongly regular general linear methods. Strongly regular A-stable general linear methods of order as high as six have been derived herein. The regularity properties of the methods are confirmed from the numerical solution of some ordinary differential equations with equilibrium points.