Again Wikipedia to the rescue.....
"Fully controlled valve movement was thought of in the earliest days of engine development, but devising a system that worked reliably, and was not overly complex, took a long time. Desmodromic valve systems are first mentioned in patents in 1896 by Gustav Mees, and in 1907 the Aries is described as having a V4 engine with "desmodromique" valve actuation, but details are scarce. The 1914 Grand Prix Delage used a desmodromic valve system (quite unlike the present day Ducati system). [1]
Azzariti, a short lived Italian manufacturer from 1933 to 1934, produced 173 cc and 348 cc twin cylinder engines, some of which had desmodromic valve gear, with the valve being closed by a separate camshaft.[2]
In 1956 Fabio Taglioni, Ducati Engineer, developed a desmodromic valve system for the Ducati 125 Grand Prix, creating the Ducati 125 Desmo. The engineers that came after him continued that development, and Ducati hold a number of patents relating to Desmodromics."