We have studied aqueous solutions of a polyelectrolyte, carboxymethylcellulose, which is an anionic cellulose derivative, and a cationic surfactant, dodecyltrimethylammonium bromido (DTAB). We have investigated the interactions between the two species, both at the air/water interface and in the bulk, for increasing DTAB concentrations. Mixed surfactant/polymer aggregates are formed at the air/water surface at extremely low surfactant concentrations, whereas bulk aggregates are formed later, above a critical aggregation concentration (cac). A small viscosity maximum at the cac reveals a small degree of bridging of the polymer chains by the surfactant. Above the cac, the viscosity drops, indicating that the polymer chains undergo a rapid collapse. At higher surfactant concentrations, light scattering shows the existence of larger structures, which are surprisingly monodisperse and whose size increases with surfactant concentration. At still higher surfactant concentrations, a classical strong associative phase separation takes place. During the evolution of bulk properties, the surface tension remains constant, suggesting that the surface aggregates remain unchanged.