The invention relates to a rim for cycles, more particular for bicycles. The invention is also aimed at a tubeless mounted assembly consisting of the said rim and of a tire having in particular two flexible bead wires. According to the invention, the rim consists of two flanges, attached to two seats, intended to receive the beads of a tire, separated from each other by a mounting groove, and, according to the profile of the rim in a radial plane, the bead seats have a generatrix, the axially outer end of which is on a circle of smaller diameter than the diameter of the circle on which the axially inner end is situated, the said generatrix forming an angle with the axis of rotation of the tire of between 15 and 45 degrees.