A propeller for an aircraft turbomachine, this propeller comprising; - a hub extending around a first axis and comprising openings distributed around this first axis, each of these openings having a substantially radial orientation with respect to said first axis and passing through said hub, - a system for controlling the angular pitch of a vane which is mounted in each of said openings, and - guide bearings (46, 48) for guiding the control system, which are mounted in each of said openings, said control system comprising: - a vane comprising a blade connected to a root, the vane comprising a pitch axis substantially radial with respect to said first axis, - a bowl extending around said pitch axis, the bowl comprising an inner housing for receiving the root of the vane, and - elements (40, 41) for attaching and securing the root of the vane against rotation with respect to the bowl, said guide bearings (46, 48) comprising: - a first ball bearing extending around said pitch axis and said root, between a radially external end of said bowl and said hub, and - a second ball bearing which extends around said pitch axis and said root, between a radially internal end of said bowl and said hub, characterised in that said second ball bearing comprises two annular rows of balls (70, 72) which are coaxial and with angular contact, a first of these rows having a first diameter and a second of these rows having a second diameter smaller than the first diameter, and characterised in that at least one plane (P1, P2) perpendicular to said pitch axis passes through the first and second rows of balls (70, 72). - a hub extending around a first axis and comprising openings distributed around this first axis, each of these openings having a substantially radial orientation with respect to said first axis and passing through said hub, - a system for controlling the angular pitch of a vane which is mounted in each of said openings, and - guide bearings (46, 48) for guiding the control system, which are mounted in each of said openings, said control system comprising: - a vane comprising a blade connected to a root, the vane comprising a pitch axis substantially radial with respect to said first axis, - a bowl extending around said pitch axis, the bowl comprising an inner housing for receiving the root of the vane, and - elements (40, 41) for attaching and securing the root of the vane against rotation with respect to the bowl, - a vane comprising a blade connected to a root, the vane comprising a pitch axis substantially radial with respect to said first axis, - a bowl extending around said pitch axis, the bowl comprising an inner housing for receiving the root of the vane, and - elements (40, 41) for attaching and securing the root of the vane against rotation with respect to the bowl, said guide bearings (46, 48) comprising: - a first ball bearing extending around said pitch axis and said root, between a radially external end of said bowl and said hub, and - a second ball bearing which extends around said pitch axis and said root, between a radially internal end of said bowl and said hub, - a first ball bearing extending around said pitch axis and said root, between a radially external end of said bowl and said hub, and - a second ball bearing which extends around said pitch axis and said root, between a radially internal end of said bowl and said hub, characterised in that said second ball bearing comprises two annular rows of balls (70, 72) which are coaxial and with angular contact, a first of these rows having a first diameter and a second of these rows having a second diameter smaller than the first diameter, and characterised in that at least one plane (P1, P2) perpendicular to said pitch axis passes through the first and second rows of balls (70, 72).