The invention concerns a drilling tool steering device, characterized in that it contains, consecutively from upstream to downstream, a main body (1) and a steerable housing (2), joined respectively by at least one connection of pivot, sliding pivot,
ball joint or annular linear type forming a first bearing (4), and at least one pivot connection forming a second bearing (5), to a bendable or flexible transmission shaft (3) which crosses them longitudinally, while a connection of pivot, sliding pivot, annular linear or
ball joint type forming a third bearing (6) between said transmission shaft and the main body (1) is arranged in proximity to the end of said main body situated in the direction of the steerable case, and while steering is carried out thanks to means acting as a deflection
system (7) for the essentially radial
relative displacement of the main body (1) in relation to the steerable housing (2) in proximity to their interface, the said main body being optionally equipped on its periphery with bearing pads (9) of
diameter less than or equal to the
diameter of the drilling tool / bit (16), and the said steerable case being optionally equipped on its periphery with bearing pads (10a) of
diameter less than or equal to the diameter of the drilling tool / bit (16) toward its end situated in the direction of the drilling tool / bit, and with fixed or expandable pads or clamps toward its end situated in the direction of the main body (1). Application to boreholes necessitating
trajectory control.