A distributed approach to perform admission control in multi-hop ad hoc networks is proposed. Existing algorithms normally compute the total amount of available resources in the network, however our method evaluates if there are sufficient resources to satisfy the bandwidth demand of a new incoming flow rather than quantifying the total amount, which is impractical when considering implementation. Our methodology also considers multi-rate scenarios and can be implemented hop-by-hop in a distributed manner, which makes the approach scalable and suitable for wireless ad hoc networks. The distributed admission control algorithm introduced in this paper is assessed via analysis and simulation.