Abstract: A method of securing a funnel-shaped guide member in the bore wall of the p-shaped casing of a self-adjusting hydraulic tappet for overhead camshaft internal combustion engines comprising first introducing a funnel-shaped guide member (2) into the bore of the cup-shaped casing (1) made of a ferrous material and being initially unhardened, the guide member (2) bearing on a shoulder (9) of the bore and then in any sequence:(a) On that side of the guide member (2) which is opposite the shoulder (9), chiplessly forming material from the bore wall so as to bear sealingly on the guide member (2) and thus to locate the same relatively to the casing (1);(b) Sealing the joint between the cup-shaped casing (1) and the funnel-shaped guide member (2) by welding or soldering.