Two compact hybrid mooring concepts adopting top synthetic fibre rope (polyester or nylon), submerged buoy and bottom chain design are studied. In addition to these two mooring concepts, another concept that adds two clumped weights on the bottom segment of the hybrid mooring with nylon rope is also studied. The mooring tension RAOs are obtained from seventeen regular wave tests to a point absorber moored by these three mooring configurations. Five spectral methods, including Dirlik, Tovo-Benasciutti, Zhao–Baker, Wirsching–Light and α0.75 methods are applied to study mooring fatigue damage. Five irregular wave model tests are performed, the rainflow counting method in conjunction with measured mooring tension time series is applied to calculate mooring fatigue damage, and the values are used to calibrate the spectral methods. The spectral methods are then used to evaluate the long term fatigue damage of these three moorings in the application in the west Portuguese coast. The rainflow counting method is applied to the mooring tension series generated from estimated mooring tension spectra to analysis fatigue damage, and the results are acted as the reference values for checking the accuracy of spectral methods. Then the performance of spectral methods is evaluated based on the Akaike's Information Criterion. •Compact hybrid mooring concepts adopting top synthetic fibre rope, submerged buoy and bottom chain design are studied.•A concept that adds two clumped weights on the bottom segment of the hybrid mooring with nylon rope is also studied.•Five spectral methods, Dirlik, Tovo-Benasciutti, Zhao–Baker, Wirsching–Light and α0.75 are applied to mooring fatigue damage.•Five irregular wave model tests are performed, the rainflow counting is applied to the measured mooring tension time series.