  This paper studies fixed-step convergence of implicit-explicit general linear
methods. We focus on a subclass of schemes that is internally consistent, has
high stage order, and favorable stability properties. Classical, index-1
differential algebraic equation, and singular perturbation convergence analyses
results are given. For all these problems IMEX GLMs from the class of interest
converge with the full theoretical orders under general assumptions. The
convergence results require the time steps to be sufficiently small, with upper
bounds that are independent on the stiffness of the problem.
