A composite connector assembly includes first and second tubular members, each constructed from fibre-reinforced polymer and each comprising at least one layer of axial or helical fibre and each comprising an end portion with a clamping surface and an overclamp. The overclamp is arranged to at least partially enclose the end portions of the first and second tubular members and to apply a clamping force to the clamping surfaces so as to connect and hold the first and second tubular members together. In each end portion, the at least one layer of axial or helical fibre is diverted radially outwards. Each end portion may have a fibre redirecting member formed underneath the axial or helical fibre which serves to divert the axial or helical fibre radially outwards.