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This paper is a description and analysis of the behaviour of a purely conceptual mechanism or system which is able to vary continuously both the opening and closing angle of internal combustion engine valves which are operated by a double overhead camshaft arrangement of substantially conventional type. The mechanism is interposed between the camshaft and the drive from the crankshaft and is able to vary the instantaneous phase of the camshaft so as to permit each cam to spend a longer or shorter time in contact with its tappet for a given engine speed. There is an implicit acceptance in the paper that published work on variable valve timing has demonstrated its desirability if the full potential of the normally aspirated internal combustion engine is to be realised. The difficulties of producing suitable mechanisms, as shown by the long history of (largely unsuccessful) interest in the subject, is acknowledged.