The invention relates to a mooring system comprising a hydrocarbon storage and/or processing unit (1) anchored to or resting on the sea bed (2) at an off shore location, and a vessel (13) moored alongside the storage and/or processing unit (1), the storage and/or processing unit (1) comprising a hull and in a front part (26) and in a rear part (25) of the unit at least one support structure (7, 7') and with another end to a quay member (10, 10') suspended from the suspension member with one end attached to the support structure (7, 7') and with another end to a quay member (10, 10') suspended from the suspension member, the quay member (10, 10') comprising a shock-absorber contacting the vessel. The quay member comprising a mooring line attachment point, a cable extending from a mooring point on the front part of the vessel and on the rear part of the vessel respectively to a corresponding mooring line attachment point on the quay member, the mooring points on the vessel and the corresponding mooring line attachment points being spaced apart in a length direction of the vessel by a distance (L1, L2) of at least 5 m, preferably at least 10 m.