A releasable connector apparatus, comprising: a connector assembly including a connector member which is moveable between connection and disconnection configurations to facilitate a releasable connection with an object; a connector mandrel comprising a support surface and being movable relative to the connector assembly such that alignment of the support surface and the connector member locks said connector member in its connected configuration, and misalignment of the support surface and the connector member permits the connector member to be moved towards its disconnected configuration; and a limit arrangement (68, 50, 78) configurable from an activated state in which movement of the connector mandrel is limited to a first range of movement over which alignment of the support surface with the connector member is maintained, to a deactivated state in which movement of the connector mandrel is permitted beyond the first range of movement to allow misalignment of the support surface and the connector member; the limit arrangement comprises an abutment member for physically limiting movement of the connector mandrel within the first range of movement, and at least one locking member (80, 82) configured to engage the abutment member and secure said abutment member at a fixed location when the limit arrangement is in its activated state, and to disengage the abutment member to deactivate the limit arrangement and permit the abutment member to be released from the fixed location; characterised in that the apparatus comprises a support member movable from a supporting position in which the at least one locking member is supported and held in engagement with the abutment member, to a desupporting position in which the at least one locking member is unsupported and permitted to disengage the abutment member; and wherein the connector mandrel and the support member are coupled together via a uni-directional coupling (90, 92) arrangement configured to permit the support member to be moved only in response to movement of the connector mandrel in one direction. a connector assembly including a connector member which is moveable between connection and disconnection configurations to facilitate a releasable connection with an object; a connector mandrel comprising a support surface and being movable relative to the connector assembly such that alignment of the support surface and the connector member locks said connector member in its connected configuration, and misalignment of the support surface and the connector member permits the connector member to be moved towards its disconnected configuration; and a limit arrangement (68, 50, 78) configurable from an activated state in which movement of the connector mandrel is limited to a first range of movement over which alignment of the support surface with the connector member is maintained, to a deactivated state in which movement of the connector mandrel is permitted beyond the first range of movement to allow misalignment of the support surface and the connector member; the limit arrangement comprises an abutment member for physically limiting movement of the connector mandrel within the first range of movement, and at least one locking member (80, 82) configured to engage the abutment member and secure said abutment member at a fixed location when the limit arrangement is in its activated state, and to disengage the abutment member to deactivate the limit arrangement and permit the abutment member to be released from the fixed location; characterised in that the apparatus comprises a support member movable from a supporting position in which the at least one locking member is supported and held in engagement with the abutment member, to a desupporting position in which the at least one locking member is unsupported and permitted to disengage the abutment member; and wherein the connector mandrel and the support member are coupled together via a uni-directional coupling (90, 92) arrangement configured to permit the support member to be moved only in response to movement of the connector mandrel in one direction.