We have grown p-type ZnCdMgSe quaternary layers and have fabricated light-emitting diodes (LEDs) from pseudomorphic quantum well (QW) structures of ZnCdSe/ZnCdMgSe grown on InP substrates that emit throughout the visible range. Nearly identical structures, differing only in the ZnCdSe QW layer thickness and/or composition can produce light ranging from blue to red. Good current-voltage characteristics are obtained from the diodes using p + ZnSeTe lattice matched to InP as the p-type contact layer. These structures have potential applications as integrated full-color display elements.