We investigate a single server system accepting two types of retrial customers and paired services. The service station can handle at most one customer, and if upon arrival a customer finds the server busy it is routed to an infinite capacity orbit queue according to its 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 only one is non-empty, then a 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, can be determined via transformation to a Riemann boundary value problem. Stability condition is investigated, while an extension of the model is also discussed and analyzed. Numerical results are obtained and yield insight into the behavior of the system. The theoretical system can be used to model a relay node for two connections in wireless communication, where network coding is used.