The exact solution of the closed queueing networks(CQN) is known only for the product form (BCMP) queueing networks. Various computational algorithms are available to derive system throughput(the rate at which a system completes units of computational work) of the networks. However, the computational expense of an exact solution is often excessive when there are multiple classes of cutomers. Instead of computing the exact values, it may be sufficient to derive bounds on the performance measures. Techniques for obtaining bounds on BCMP queueing networks have appeared in the past years. This paper also presents bounds on throughput in CQN models with multiple classes of customers.