A characterisation of ZnSe-based Schottky barrier photodetectors grown by molecular beam epitaxy is presented. High quality diodes exhibiting a high responsivity of 0.01 A/W at 455nm and a sharp cut-off of three to four orders of magnitude have been fabricated. A detectivity of 1.4 x 10(10) mHz(1/2)W(-1) has been obtained for a structure with a 5mm(2) area operating at -3.5V bias. These results highlight the potential of ZnSe in blue and near-ultraviolet light detection.