The present work combines the advantages of using highly active Pt together with low cost transition metals, like Co, Ni, and Cu, in bimetallic alloy nanoparticles along with the employment of reduced graphene oxide (rGO) as an efficient carbon-based electrocatalyst support. Thus, Pt and three different MPt (M = Ni, Co, Cu) alloy nanoparticles supported on rGO were synthesized, characterized (by TEM and ICP-MS), and assessed as electrocatalysts for hydrogen production by alkaline water electrolysis. The evaluation of HER kinetics at the MPt/rGO composites was done by linear scan voltammetry measurements in 8 M KOH solution. Higher current densities were achieved for the MPt/rGO electrocatalysts (in comparison with the monometallic one, Pt/rGO), with considerably lower Tafel slopes. It was observed that increasing the temperature up to 338 K leads to a substantial increase of HER current densities at all electrocatalysts. The corresponding Arrhenius analysis showed that HER activation energies in the rGO-supported electrocatalysts ranged between 27.5 and 36.7 kJ mol-1.