Diagonally implicit general linear methods for ordinary differential equations

We investigate some classes of general linear methods with s internal and r external approximations, with stage order q and order p, adjacent to the class with s=r=q=p considered by Butcher. We demonstrate that interesting methods exist also if s+1=r=q, p=q or q+1, s=r+1=q, p=q or q+1, and s=r=q, p=q+1. Examples of such methods are constructed with stability function matching the A-acceptable generalized Padé approximations to the exponential function.