We demonstrate a passively mode-locked femtosecond Yb:KLu(WO(4))(2) thin-disk laser oscillator. Chirped-pulse operation in the positive dispersion regime as well as solitary operation have been realized, and the laser performance of both configurations are compared. In the solitary mode-locking regime the output power exceeds 25 W in a diffraction-limited beam, and pulse durations as short as 440 fs at a 34.7 MHz repetition rate have been generated. For the first time we present a chirped-pulse operation of a thin-disk oscillator that yields a maximum average output power of 9.5 W with a Fourier limit of 450 fs.