Copper and copper alloys are prevented from rust by surface-treating the copper and copper alloys with at least one compound selected from the class consisting of alkylimidazoles represented by the following formula: ##SPC1##Wherein R is a long straight chain alkyl group of 5-21 carbon atoms and R' is hydrogen atom or a lower alkyl group, and their acid addition salts. The compound is used as it is, or in a solution, by dipping, spraying, coating or directly contacting with copper or copper alloy. The surface -treated copper and copper alloy can well withstand tarnishing in an atmosphere containing sulfur compound gas.