We report on the first demonstration of a passively (SESAM) mode-locked Yb:CaF(2) thin-disk laser operating at a repetition rate of 35 MHz with close to diffraction-limited beam quality (M(2) ≈ 1.1) at an average output power of up to 6.6 W. The optical efficiency was 15.3%. Nearly transform limited pulses with a duration of 445 fs and a spectral width of 2.6 nm at full width half maximum (FWHM) were obtained at the maximum output power. This corresponds to a pulse-energy of approximately 0.19 μJ and a peak-power of 0.4 MW.