Various A-stable and L-stable methods for the solution of stiff systems of ordinary differential equations are surveyed. While DIRK methods are attractive because of their low implementation costs, they suffer other disadvantages, such as limited stage-order. It is shown that it is possible to extend the diagonally-implcit structure to general linear methods, so as to achieve high stage order. The crucial assumption made in this presentation is a new property known as Inherent Runge-Kutta Stability. This simplifies stability considerations and enables methods to be found routinely, in a way that is not possible, for example, with DIMSIM methods. Some of the implementation issues associated with the new methods will be discussed.