The refrigerant chemicals used in conventional vapour-compression heatpumps and refrigerators all have one or more of the following drawbacks: flammability, toxicity, ozone depletion: and/or global warming potential. This thesis investigates an alternative type of heat-pump and refrigerator based on the Stirling cycle. Stirling-type systems offer an important advantage in that they can operate using only air as the refrigerant. Practical Stirling machines are generally thought to have the potential for much higher efficiency than conventional vapour-compression systems. The first part of this thesis re-examines this conclusion: and proposes an alternative thermodynamic analysis which indicates that this is not actually the case. On a more positive note, however, the analysis also indicates that real Stirling heat-pumps may provide a slight advantage over vapour-compression machines in terms of a more consistent heat production capability. The second part of this thesis describes the manufacture of a prototype Stirling system, and the testing of this prototype under typical heat-pump operating conditions. Cost was minimized in this design by utilizing plastics components, inexpensive rubbing seals, and a kinematic mechanism from a mass-manufactured Stirling engine. The measured efficiency of the prototype was only about the same as for a high-efficiency vapour-compression heat-pump, and it was therefore concluded that this approach provided insufficient performance advantages to be commercially competitive. It was found that the performance of the prototype was primarily limited by the geometric constraints of the mass-manufactured kinematic mechanism. An alternative design is therefore proposed which permits much higher performance by utilizing a double scotch-yoke kinematic mechanism. The final part of this thesis proposes a new variation on standard Stirling systems. A novel open regenerative cycle machine is presented which appears to offer a number of potential cost and performance advantages in heat-pump and refrigerator applications.