A hinge assembly has first and second parts pivotally connected together. One of the parts has a hinge cup (13) and is connectable to a first element such as a cupboard door. The other part is connectable to a second element such as the cupboard carcase. The assembly includes a linear damping device (17), which is actuable to provide a damped resistive force over at least part of the range of relative pivotal movement between the two hinge elements. The linear damping device (17) is conveniently mounted within the hinge cup (13).