The dielectric operator for non-homogeneous plane-parallel cold plasma flows in an external magnetic field is given. The potential oscillations of two sliding plasmas are investigated. Expressions for the energy transfer between the plasmas, and the energy of the modes, are derived. A group-velocity analysis shows that pair emission of negative and positive energy waves occurs for modulation along the flow. Transverse modulation leads to an overstability of the system. A connection between the radiated plasma resonances and the overstability is worked out. Regions of existence and properties of the unstable modes are discussed in detail. For oblique modulations the regions of existence of unstable modes show marked departures from the already known results for parallel modulation.