The electrochemical impulse oscillations of the cathodic currents at the platinum group (Pt, Pd) electrode/(0.05M KHC$_{8}H_{4}O_{4}$) buffer solution interfaces have been studied using voltammetric, chronoamperometric, and electrochemical impedance methods. The periodic impulses of the cathodic currents are the activation controlled currents due to the hydrogen evolution reaction, and depend on the fractional surface coverage of the adsorbed hydrogen intermediate and potential. The oscillatory mechanism of the cathodic current impulses is connected with the unstable steady state of negative differential resistance. The widths and periods of the cathodic current impulses are 4ms or 5ms and 152.5ms or 305ms, respectively. The H$^{+}$ discharge reaction step is 38 or 61 times faster thatn the recombination reaction steps and the H$^{+}$ mass transport processes. The atom-atom recombination reaction step is twice faster thatn the atom-ion recombination reaction step. The two kinds of active sites corresponding to the atom-atom and atom-ion recombination reaction steps exist on the platinum group electrode surfaces.