NOVELTY - An anodic (intended for fuel oxidation) and cathodic (intended for oxygen reduction) core-shell electrocatalyst is made of supported mono- and plurimetallic carbon nitride cluster as shell. The support consists of electroconductive nanoparticles of graphite powder or platelet, and powder of specific metal as core.    USE - Anodic and cathodic core-shell electrocatalyst is used in polymer electrolyte membrane fuel cell, direct methanol fuel cell, alkaline fuel cell, phosphoric acid fuel cell and hydrogen electrolyzer.    ADVANTAGE - The anodic and cathodic core-shell electrocatalyst has favorable electrical conductivity.    DETAILED DESCRIPTION - An anodic (intended for fuel oxidation) and cathodic (intended for oxygen reduction) core-shell electrocatalyst is made of supported mono- and plurimetallic carbon nitride cluster as shell. The support consists of electroconductive nanoparticles of graphite powder or platelet, and powder of metal (M) as core. The metal (M) is chosen from titanium, silver, gold, platinum, zirconium, manganese, tungsten, lead, scandium, vanadium, iron, cobalt, nickel, zinc, bismuth, copper, chromium, yttrium, niobium, molybdenum, ruthenium, rhodium, palladium, cadmium, lutetium, hafnium, tantalum, tungsten, rhenium, osmium, iridium, lanthanum, cerium, praseodymium, neodymium, samarium, europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium, gallium, indium, thallium, silicon, germanium or tin. INDEPENDENT CLAIMS are included for the following:    (1) manufacture of anodic and cathodic core-shell electrocatalyst. A precursor is prepared and subjected to thermal treatment. The treated product is activated by chemical and/or electrochemical method to obtain electrocatalyst;    (2) manufacture of precursor which involves mixing two solutions (A,B) through sol-gel reaction; and    (3) activation of electrocatalyst, which involves electrochemical process simulating cyclic voltammetry method in presence of inert gas such as nitrogen and argon, alternated to oxidant gas such as oxygen and/or reducing agent such as hydrogen and hydrazine.