The invention relates a bi-lumen (double-lumen) breathing circuit assembly for use in medical anaesthesia. The assembly comprises first and second breathing circuit conduit lengths (1, 11) each comprising: (i) a lengthwise extending inner septum (12) for segregating inspiratory and expiratory lumens (110) and (ii) lumen opening pairs at their respective opposite distal ends (21). The assembly further comprises a connector (2) comprising: (iii) a lengthwise extending connector septum (24) for segregating inspiratory and expiratory connector passages (50, 60) and (iv) a pair of connector openings at its respective opposite distal ends. A concavity (70) is provided at each distal end of the connecting septum for receiving an inner septum (12) of each breathing circuit conduit length (1, 11) in a secure, airtight manner. This ensures a contiguous passage between connected lengths of breathing circuit conduits (1, 11) via a range of different connectors or adapters (2) having different shapes and functions.