A gas-cycle system operable using a Bell-Coleman cycle, the gas-cycle system comprising an expander (23) and a compressor (27) incorporated in a flow path (13). The expander (23) and compressor (27) are integrated in a rotary machine (41), and each comprises a rotor assembly (70) configured to define one or more zones (80) each of which changes continuously in volume during a rotation cycle of the rotor assembly. The expander (23) and compressor (27) are drivingly interconnected whereby rotational drive applied to one is transmitted directly to the other. Each rotor assembly (70) comprises an inner rotor (73) and an outer rotor (75) adapted to rotate about parallel axes at different rotational speeds. The inner rotors (73) are each drivingly connected to a common shaft for rotation therewith. The two outer rotors (75) are coupled together such that rotational drive applied to one is transmitted directly to the other. An air-cycle system and an air conditioning system (10) based on the gas-cycle system are also disclosed.