A conveyor apparatus, so-called injector head, to enable feeding of continuous elongate device (7; CED), e.g. continuous tubing or coiled tubing, down through the conveyor apparatus, to enable insertion of tools through the wellhead and a well below, or up through the conveyor apparatus by pulling action enabling retrieval of the tool from the wellhead and the well below, the conveyor apparatus comprising: an apparatus frame, a pair oppositely located, co-operatively movable, segmented continuous belts (28; 29) installed in the frame, each belt comprising a plurality of interconnected device gripper shoe carriers carried and movable by means of a pair of continuous belt drive chains (31; 32) running over respective pairs of chain drive sprockets (33: 34), wherein each carrier has a front side and a rear side (30"), wherein the rear side (30") of the carrier has at least one roller configured to roll about a shaft attached to the carrier against an elongate counter-force member associated with the frame and extending between said drive sprockets (33; 34), and wherein a device gripper shoe (38; 52) is located at the front side of each carrier, characterized in that the shaft of the at least one roller is resiliently supported transversely of its longitudinal axis by means of a plurality of resilient members fitted onto or about the shaft in the rear side (30") of the carrier to lie about the shaft at spaced apart locations, each resilient member being: - a customized metal spring; or - made of rubber or another elastomeric material; or - an oblong or elliptical member with curved ends and having its hole off-center or located eccentrically, wherein a plurality of slits is provided providing a spring feature; or - a coiled spring; or - a disc spring. an apparatus frame, a pair oppositely located, co-operatively movable, segmented continuous belts (28; 29) installed in the frame, each belt comprising a plurality of interconnected device gripper shoe carriers carried and movable by means of a pair of continuous belt drive chains (31; 32) running over respective pairs of chain drive sprockets (33: 34), wherein each carrier has a front side and a rear side (30"), wherein the rear side (30") of the carrier has at least one roller configured to roll about a shaft attached to the carrier against an elongate counter-force member associated with the frame and extending between said drive sprockets (33; 34), and wherein a device gripper shoe (38; 52) is located at the front side of each carrier, characterized in that the shaft of the at least one roller is resiliently supported transversely of its longitudinal axis by means of a plurality of resilient members fitted onto or about the shaft in the rear side (30") of the carrier to lie about the shaft at spaced apart locations, each resilient member being: - a customized metal spring; or - made of rubber or another elastomeric material; or - an oblong or elliptical member with curved ends and having its hole off-center or located eccentrically, wherein a plurality of slits is provided providing a spring feature; or - a coiled spring; or - a disc spring. - a customized metal spring; or - made of rubber or another elastomeric material; or - an oblong or elliptical member with curved ends and having its hole off-center or located eccentrically, wherein a plurality of slits is provided providing a spring feature; or - a coiled spring; or - a disc spring.