A substrate, such as a catheter or a guide wire, or a portion of the substrate is provided with a lubricous, hydrophilic abrasion-resistant coating by: (a) coating the substrate with a first aqueous coating composition having an aqueous dispersion or emulsion of a polymer having organic acid functional groups and a polyfunctional crosslinking agent having functional groups capable of reacting with organic acid groups, and drying the coating to obtain a substantially water-insoluble coating layer having excess polyfunctional including functional groups being reactive with organic acid groups remaining; and (b) contacting the dried water-insoluble coating layer with a second aqueous coating composition having an aqueous solution or dispersion of a hydrophilic polymer having organic acid functional groups, a polymer having organic acid functional groups and a polyfunctional crosslinking agent having functional groups capable of reacting with organic acid groups, and drying the combined coating to form an intermediate coating, whereby the polymer and the hydrophilic polymer of the second composition become bonded to the polymer of the first coating composition through the excess crosslinking agent; and (c) contacting the dried intermediate coating with a third aqueous coating composition having an aqueous solution or dispersion of a hydrophilic polymer having organic acid functional groups, and drying the combined coatings, the hydrophilic polymer of the third coating composition thereby becoming bonded to the polymers of the second coating composition through the excess crosslinking agent. The dryings can be carried out at ambient (room) temperature.