We report the detection of oscillations in slender Ca II H fibrils (SCFs) from high-resolution observations acquired with the Sunrise balloon-borne solar observatory. The SCFs show obvious oscillations in their intensity, but also their width. The oscillatory behaviors are investigated at several positions along the axes of the SCFs. A large majority of fibrils show signs of oscillations in intensity. Their periods and phase speeds are analyzed using a wavelet analysis. The width and intensity perturbations have overlapping distributions of the wave period. The obtained distributions have median values of the period of $32pm17$s and $36pm25$s, respectively. We find that the fluctuations of both parameters propagate in the SCFs with speeds of ${11}^{+49}_{-11}$ km/s and ${15}^{+34}_{-15}$ km/s, respectively. Furthermore, the width and intensity oscillations have a strong tendency to be either in anti-phase, or, to a smaller extent, in phase. This suggests that the oscillations of both parameters are caused by the same wave mode and that the waves are likely propagating. Taking all the evidence together, the most likely wave mode to explain all measurements and criteria is the fast sausage mode.
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