p-type ZnSe layers have been successfully grown by molecular beam epitaxy using remote microwave plasma of N2. The net acceptor concentration N(A)-N(D) in the layer from 1.5 X 10(16) to 1.2 X 10(18) CM- 3 has been controlled by adjusting the flow rate of N2, the input microwave power and the substrate temperature. At a doping level of N(A)-N(D) = 1.5 X 10(16) cm-3, the photoluminescence at 4.2 K was characterized by an acceptor bound exciton at 444.3 nm (2.790 eV), a free electron to acceptor hole (FA) emission with a zero phonon line (ZPL) at 457.3 nm (2.710 eV) and a donor-acceptor pair (DAP) emission with a ZPL at 459.9 nm (2.695 eV). However, if N(A)-N(D) exceeds 10(17) CM-3, the different series of DAP with a ZPL at 463.0 nm (2.677 eV) dominated the spectra, indicating some compensation occurring in the sample. The deep level transient spectroscopy revealed a deep hole trap level, whose activation energy was determined as 0.67 eV.