In this talk we consider issues related to the solution of large-scale, nonlinear, multiple-time-scale, PDE systems. We begin by reviewing a number of solution strategies for such systems, including time-integration techniques based on time-step lagging and linearization of nonlinear terms, various operator-splitting methods and fully-implicit techniques. These techniques have been applied to a set of diffusion/reaction problems: thermal-wave propagation, chemical dynamics and radiation/diffusion. We will comment on the time accuracy, the nonlinear consistency and the apparent stability of these methods. We will also describe some difficulties of completing order-of-accuracy studies between solution methods due to differences in the behavior of the effective spatial discretization of the PDEs. -------------------------- (1) This work was partially supported by the DOE office Science MICS effort and the ASCI Algorithms effort at Sandia National Laboratory under contract DE-AC04-94AL85000 (2) Computational Sciences Department (3) Computational Mathematics and Algorithms Department --