Aeroplane tyre comprising: - a tread connected by two side walls to two beads, which are intended to provide a mechanical connection between the tyre and a rim, - a crown reinforcement, radially on the inside of the tread, and a carcass reinforcement radially on the inside of the crown reinforcement, - the carcass reinforcement comprising a first and a second family of carcass layers (51, 52) extending between the two beads, - the first family comprising at least one carcass layer wrapped, within each bead, from the inside towards the outside of the tyre, around a circumferential reinforcing element known as a bead wire to form a turn-up having a free end (E 1) radially on the outside of the radially outermost point of the bead wire, - the second family comprising at least two carcass layers, adjacent each to the next, extending, within each bead, from the outside towards the inside of the tyre, as far as their respective ends (E 2) which are radially on the inside of an axial straight line (D Y) passing through the centre of the bead wire and axially on the inside of a radial straight line (D Z) passing through the centre of the bead wire at an axial distance (d 2) at least equal to 5 mm, - the carcass layers of the second family being axially on the inside of at least one turn-up of a carcass layer of the first family, - the reinforcing elements of a carcass layer (51, 52) being made of textile materials, any textile reinforcing element of any carcass layer (51, 52) being obtained by twisting, in the clockwise direction, at least two overtwists, each overtwist being obtained by twisting, in the anticlockwise direction, a spun fibre consisting of mutually parallel textile filaments, this twisting being defined by a number of twists per metre referred to as overtwisting, characterized in that the overtwisting, to obtain overtwists of the textile reinforcing elements of the carcass layers (51, 52), is at least equal to 250 turns/metre and at most 290 turns/metre. - a tread connected by two side walls to two beads, which are intended to provide a mechanical connection between the tyre and a rim, - a crown reinforcement, radially on the inside of the tread, and a carcass reinforcement radially on the inside of the crown reinforcement, - the carcass reinforcement comprising a first and a second family of carcass layers (51, 52) extending between the two beads, - the first family comprising at least one carcass layer wrapped, within each bead, from the inside towards the outside of the tyre, around a circumferential reinforcing element known as a bead wire to form a turn-up having a free end (E 1) radially on the outside of the radially outermost point of the bead wire, - the second family comprising at least two carcass layers, adjacent each to the next, extending, within each bead, from the outside towards the inside of the tyre, as far as their respective ends (E 2) which are radially on the inside of an axial straight line (D Y) passing through the centre of the bead wire and axially on the inside of a radial straight line (D Z) passing through the centre of the bead wire at an axial distance (d 2) at least equal to 5 mm, - the carcass layers of the second family being axially on the inside of at least one turn-up of a carcass layer of the first family, - the reinforcing elements of a carcass layer (51, 52) being made of textile materials, any textile reinforcing element of any carcass layer (51, 52) being obtained by twisting, in the clockwise direction, at least two overtwists, each overtwist being obtained by twisting, in the anticlockwise direction, a spun fibre consisting of mutually parallel textile filaments, this twisting being defined by a number of twists per metre referred to as overtwisting,