Abstract: We consider coexistence of two overlapping Ad Hoc networks: the primary network and secondary network. Nodes in each network are random and independently distributed according spatial Poisson point process with different densities, and different transmission probabilities are assumed for the nodes in each network according slotted-ALOHA protocol. When the two networks coexist, throughput in each network is limited by the self interference as well as the interference from the other network. In this paper, the interference for each network node is modeled as a simple Gaussian random variable which is equal to the sum of the interference not only from its own network but also from the other network, and based on stochastic geometry theory, closed-form expression of per-node throughput capacity is derived for single Ad Hoc network and overlapping Ad Hoc networks under AWGN channel and Rayleigh faded channel respectively. Optimization criteria are used to find the optimal transmission probability in each network to satisfy the expected performance. Simulation verified the theory analyses and results show that there is a tradeoff between high utilization and fairness when proportional fairness criterion is used.