We develop an analytical theory for edge states in monolayers of transition metal dichalcogenides based on a general boundary condition for a two-band kp Hamiltonian in the case of uncoupled valleys. Taking into account edge spin-orbit interaction, we reveal that edge states, in general, have linear dispersion that is determined by three real phenomenological parameters in the boundary condition. In the absence of the edge spin-orbit interaction, edge states are described by a single real parameter whose sign determines whether their spectra intersect the bulk gap or not. In the former case we show that illumination by circularly polarized light results in spin- and valley-polarized photocurrent along the edge. Flow direction and spin and valley polarization of the edge photocurrent are determined by the direction of circular polarization of the illuminated light.