Mode locking based on an epitaxial composite of the monoclinic double tungstate crystal Yb:KLu(WO4)2 is realized. A 100 microm thin Yb:KLu(WO4)2 layer grown on a KLu(WO4)2 substrate is used as an active medium in a laser passively mode locked by a semiconductor saturable absorber. Pulse durations of 114 fs have been achieved for an average power of 31 mW at 1030 nm. Results in the femtosecond and picosecond regimes of the Yb:KLu(WO4)2/KLu(WO4)2 laser are presented. The great potential of Yb-doped tungstate composite structures as active elements for mode-locked laser systems is demonstrated.