A wheel construction (10) includes a wheel rim (11) which in use receives a (tyre 14), the rim (11) having axially inner and outer portions (16, 15), and a mid-portion (18) between them, and each axially inner and outer portion (16, 15) providing a
flange (22), a connecting surface (23) adjoining the
flange (22) and extending axially towards the mid portion (18), the
flange (22) and a part of theconnecting surface (23) providing a seat for a bead of the tyre (14), and there being a side part (19, 20) between the connecting surface (23) and the mid portion (18), and wherein for at least one of the inner and outer portions (16, 15), the connecting surface (23) is a frusto-conical having an axial end (24) of greatest
radius and an axial end (25) of least
radius, the connecting surface (23),at its axial end of greatest
radius (24), adjoining the flange (22), and the axial end (25) of least radius adjoining a circumferentially extending convex surface (26) which extends radially outwardly of the wheel axis A beyond the end (25) of least radius of the adjoining frusto-conical connecting surface (23), and the side part (19, 20) of the at least one of the axially inner and outer portions (16,15) including a generally frusto-conical region (28) and a curved region (40), the curved region (40) including first and second axially spaced circumferentially extending concave surfaces (41, 42), and the curved region (40) adjoining the end of least radius of the frusto- conical region (28) and the mid-portion (18).