The invention is a method for the production of a composite multilayer material having a backing layer, a bearing metal layer of a copper alloy or an aluminum alloy, a nickel intermediate layer and an overlay consisting of about 0-20 wt. % copper and about 0-20 wt. % silver, the combined maximum wt. % of copper and silver being about 20 wt. %, the rest being bismuth, and the layer thickness of the nickel layer amounts to more than 4 .mu.m by electrodeposition, in which the overlay is deposited from methyl sulphonic acid-based electrolyte.