The aim of this dissertation is to develop approximations to performance measures for queues with synchronization constraints with the help of limit theorems. In particular we shall consider queues exhibiting the fork-join and resequencing constraints. These queues invariably exhibit non-product form behavior, and their analysis by any other method is extremely difficult. The limit theorems that we shall use come in two flavors, i.e. heavy traffic limit theorems and light traffic limit theorems. Heavy traffic limit theorems give estimates of the performance measures when the system is operating near its full capacity, while light traffic limit theorems give estimates of the performance measures when the system is very lightly loaded. By interpolating between these two limits it is possible to obtain estimates of the performance measure when the system operates at moderate loads.