Graphene and its analogs in combination with metal nanopowders are among the most promising catalysts for various industry valuable processes. The newly obtained solution combustion synthesized graphene-Cu and graphene-CuNi nanocomposites were examined in heterogeneous catalysis of thermal activated CO oxidation and photoactivated degradation of acid telon blue and direct blue dyes. The nanocomposites are characterized by a closely connected solution combustion synthesized graphene-metal structure with a number of graphene layers from 1 to 3 and fine metal grains sizes of 31 nm (Cu) and 14 nm (CuNi). The experimental data showed the obtained graphene-metal nanocomposites are among the most effective catalysts for CO oxidation with a temperature of 100% conversion of 150 °C and 200 °C for Cu and CuNi containing catalysts, respectively. At the same time, both nanopowders were found inactive for dyes degradation.