A wheel construction (10) includes a wheel rim (11) which in use, at a tire side (12) of the rim (11), receives a tire (14), the rim (11) being circular and having axially inner and outer portions (16,15), and a mid-portion (18) between the axially inner and outer portions (16,15), the mid-portion (18) including a circumferential well where the radius of the wheel rim (11) is a minimum, 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 the connecting surface (23) providing a seat for a bead of the tire (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 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 (24) of greatest radius, adjoining the flange (22), and the side part (20, 19) 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 frusto-conical region (28) at its end of greatest radius (26) adjoining the connecting surface (23), and the curved region (40) including first (41), second (42) and third (43) axially spaced circumferentially extending concave surfaces, when viewed from the tire side (12) of the rim (11), the curved region (40) adjoining an end (29) of least radius of the frusto-conical region (28) and the mid-portion (18).