Wemathematically investigate a single server system accepting two types of retrial customers and paired service. If upon arrival a customer finds the server busy, it is routed to an infinite capacity orbit queue according to each type. Upon a service completion epoch, if at least one orbit queue is non-empty, the server seeks to find customers from the orbits. If both orbit queues are non-empty, the seeking process will bring to the service area a pair of customers, one from each orbit. If there is only one non-empty, then a single customer from this orbit queue will be brought to the service area. However, if a primary customer arrives during the seeking process it will occupy the server immediately. It is shown that the joint stationary orbit queue length distribution at service completion epochs is determined by solving a Riemann boundary value problem. Stability condition is investigated, while generalizations of themainmodel are also discussed. A simple numerical example is obtained and yields insight into the behavior of the system.