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Diode-pumped soliton and non-soliton mode-locked Yb:(Gd1-xYx,)2SiO5 (x=0.5) lasers are demonstrated.Pulsesas short as 1.4 ps are generated for the soliton mode-locked operation, with a pair of SF10 prisms as the negativedispersion elements.The central wavelength is 1056nm and the repetition rate is 48 MHz.For the non-solitonmode locking, the output power could achieve ～1.2W and the pulse width is about 20ps.The critical pulseenergy in the soliton-mode locked operation against the Q-switched mode locking is much lower than the criticalpulse energy in the non-soliton mode-locked operation