A process for producing a pyrazine compound of the general formula (3): ##STR1## wherein R.sup.1, R.sup.2, R.sup.3 and R.sup.4 represent a hydrogen atom or a lower alkyl group, which comprises catalytically reacting in a gaseous phase a diamine compound of the general formula: ##STR2## with a diol compound of the general formula: ##STR3## in the presence of a catalyst containing hydrogen-treated silver or a catalyst containing silver and at least one element selected from the group consisting of alkali metals, alkaline earth metals, zinc and lanthanoid elements.