Graphics cards, traditionally designed as accelerators for computer graphics, have evolved to support more general-purpose computation. General Purpose Graphical Processing Units (GPGPUs) are now being used as highly efficient, cost-effective platforms for executing certain simulation applications. While most of these applications belong to the category of timestepped simulations, little is known about the applicability of GPGPUs to discrete event simulation (DES). Here, we identify some of the issues & challenges that the GPGPU stream-based interface raises for DES, and present some possible approaches to moving DES to GPGPUs. Initial performance results on simulation of a diffusion process show that DES-style execution on GPGPU runs faster than DES on CPU and also significantly faster than time-stepped simulations on either CPU or GPGPU.