A device for increasing the stability of a helicopter having a tricycle landing gear (2, 6) constituted by two main and lateral undercarriages (6) and one auxiliary undercarriage (2) when said helicopter is set down on a moving platform, said device comprising an auxiliary stabilizing gear operative only when said helicopter is landing with a rotor thereof rotating or stopped, said stabilizing gear comprising at least two lateral stabilizers (13), each of said lateral stabilizers comprising a rigid support (17, 27) having an end part which supports at least one stabilizing wheel (16) for contact with said platform, said rigid support (17, 27), at least in position of use, being integral with a stable structure of said helicopter at a lower part of a fuselage (1) of said helicopter, said rigid supports being offset laterally one on each side of a vertical and median longitudinal plane (PP) of said helicopter, in the direction turned towards and auxiliary undercarriage (2) in relation to said main an lateral undercarriages (6) of said tricycle landing gear, in such a manner that said at least one stabilizing wheel (16) is supported on said moving platform, on both sides of said longitudinal and median plane of said helicopter (PP) when said helicopter rests on said platform with said tricycle landing gear (2, 6), wherein each lateral stabilizer (13, 43) comprises a mechanism for regulating the height of at least one stabilizing wheel (44') in relation to the fuselage, said mechanism comprising a toothed wheel (111) operated by a crank (121) and in engagement with a pinion (109) for entrainment in rotation of an endless screw (101), in an axial position fixed in relation too the tubular shaft (47') in which it is at least partially accommodated and in engagement with a slider (68) guided in axial translation in said tubular shaft (47') and in which a spindle (48') supporting the stabilizing wheel or wheels (44') is mounted so as to turn.