The results of experiments concerning the irradiation of copper and Cu-10% Ga alloys by pulsed fluxes of deuterium plasma (DP) and deuterium ions (DI) performed using a Plasma Focus (PF) unit are presented. The technique of investigation is described. Damage and deformation effects in the surface layers of the mentioned materials after the irradiation of each material in two modes are studied. In one case, the irradiation is performed by a pulsed deuterium plasma at a power density of qpl = 107 W/cm2 and at pulse duration of τpl = 100 ns. In another case, the pulsed fluxes of deuterium ions at qi = 108–1011 W/cm2, τi = 50 ns act simultaneously with a dense deuterium plasma at qpl = 108–109 W/cm2, τpl = 100 ns. Under a less severe irradiation mode (only plasma flux), the levels of damage in the case of both materials are close to each other. In the melted surface layer (SL), there are an undulated surface, craters, and micropores. Under the influence of thermal stresses, a plastic deformation is observed in the SL of the alloy, whereas in the case of pure copper this process is not observed under this irradiation mode. Damage to both materials in a more severe irradiation mode with the pulsed fluxes of deuterium ions and deuterium plasma is enhanced and accompanied by the SL erosion and sometimes by a deposition of microparticles of elements contained in the functional materials of the PF chamber onto the irradiated surface. The most significant damage is observed in the SL of Cu–10% Ga alloy, which, along with the action of powerful plasma beam fluxes, experiences a shock-wave impact. In this irradiation mode, plastic deformation is observed in the SL of each of the materials under consideration. In the case of pure copper (at q = 108–109 W/cm2), the plastic deformation is observed in separate local microvolumes of SL, whereas in the case of copper-gallium alloy at q = 1010–1011 W/cm2 this process occurs within the entire irradiated SL. In this case, plastic deformation occurs both under the action of shock-wave mechanical loads and under the action of thermal stresses.