Abstract: Method and apparatus of coating a plurality of wet layers on an flexible elongated web, which is economical to build and easy to operate at high speeds, and an apparatus which can be used to manufacture multi-layer magnetic recording media of the highest quality. Such apparatus can employ a gravure coater while an extrusion die both smoothes the wet gravure layer to eliminate its pattern and simultaneously extrudes a second dispersion. That smoothing is provided by a face of the upstream lip, which face has a convex shape that allows the wet gravure layer to remain in contact with the upstream lip over a wrap angle .gamma. of at least two degrees, thus ensuring that the tensioned carrier web neither buckles in the cross-web direction nor experiences instabilities such as fluttering. The extruded layer is contacted by a smooth face of the downstream lip, and the coated carrier web exits the smooth face substantially tangentially at a sharp trailing corner.