In this paper, we study the service exchange problem where each agent is willing to provide her service in order to receive in exchange the service of someone else. We assume that agent's preference depends both on the service that she receives and the person who receives her service. This framework is an extension of the housing market problem to preferences including a degree of externalities. We investigate the complexity of computing an individually rational and Pareto efficient allocation of services to agents for ordinal preferences, and the complexity of computing an allocation which maximizes either the utility sum or the utility of the least served agent for cardinal preferences.