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We report high power continuous-wave (CW) and passively mode-locked lasers with Yb,Na:CaF2 crystal as gain material. A maximum CW output power of 14.5 W was achieved at the absorbed pump power of 22.8 W, corresponding to the slope efficiency of 63.6%. Furthermore, by using a semiconductor saturable absorber mirror, the CW mode-locking operation was achieved. A shortest duration of 175 fs with the average power of 352 mW, and a highest average power of 510 mW with duration of 190 fs were obtained. The dynamics of soliton mode-locking in the laser concerned with the absorbed pump power and the intra-cavity negative group delay dispersion were experimentally investigated.