Process coordination problems have been extensively addressed in the context of sequential consistency. However, modern multiprocessors present a large variety of memory models that are anything but sequentially consistent. In these machines, the ordering constraints on memory accesses are few. We re-address two fundamental process coordination problems in the context of weak memory models. We prove that many models cannot support a solution to the critical section problem without additional powerful synchronization primitives. Nevertheless, we show that certain versions of the producer/consumer problem can be solved even in the weakest models without the need for such powerful instructions. These instructions are expensive, and avoiding their use is desirable for better performance.