A trampoline has an enclosure system including a barrier of a flexible material (14) such as a net material surrounding the trampoline mat above the mat and having a lower peripheral part coupled directly or indirectly to the mat, and a plurality of resiliently flexible generally upright enclosure support members or rods (13) which are retained at or towards the lower ends of the enclosure support members and below the mat (1) by the frame (4) of the trampoline and which support the net above the mat, so that the enclosure is free to deform away from the mat when impacted by a user against an enclosure support member and/or against said barrier of flexible material.