A system for continuously varying valve-opening overlap in reciprocating internal combustion engines changes the path of the timing belt (16) that drives the intake valve camshaft (26). An idler wheel (44) mounted on a pivoted arm (48) turns against the timing belt. At low engine speeds, the sprocket wheel idles against the timing belt. At higher engine speeds, increased engine oil pressure causes a hydraulic cylinder (58) to force the sprocket wheel against the timing belt, changing its path. As the path of the belt is changed, the intake valve position is advanced with respect to the position of the crankshaft (12). The exhaust valve position remains the same relative to that of the crankshaft. Thus at above-idle speeds, intake-exhaust valve overlap is present. Since the amount of belt path deviation is related to engine oil pressure, and thus engine speed, valve overlap varies smoothly as a function of engine speed. A tensioner (30) maintains proper belt tensioning at all times.