Abstract: A high-speed bevel gear transmission system for transmitting power from an input shaft to a pair of parallel outputs shafts the axes of which intersect each other. The input shaft has a pair of driving bevel gears which are fixedly mounted thereon such that the driving bevel gears face in opposite directions and which have the same number and size of teeth spirally arranged in the opposite directions each other. The output shafts are supported on angular contact ball bearings and have two driven bevel gears fixedly mounted thereon which are engaged with the driving bevel gears. The speed transmission ratio of the output shafts to the input shaft is 1.45:1 to 0.476:0.1, the relation between a pressure angle .alpha. and helix angle .beta. of the driving bevel gears and driven bevel gears, and a pitch cone angle .delta. of the driven bevel gears are defined by the formula, R=[(tan.alpha..multidot.sin .delta.)/cos .beta.]-tan.beta..multidot. cos .delta. when 0.324.ltoreq.R.ltoreq.0.1.