In this paper we consider general simulations of algorithms designed for fully operational BSP and CGM machines on machines with faulty processors. The faults are deterministic (i.e., worst-case distributions of faults are considered) and static (i.e., they do not change in the course of computation). We assume that a constant fraction of processors are faulty. We present a deterministic simulation (resp. a randomized simulation) that achieves constant slowdown per local computations and Ǵ