Using high-resolution oxygen A band spectrometry (λ/Δλ = 60000) in the 767.7--770.7 nm wavelength range, we investigate the first and second moments of the distributions of path lengths of photons in transmitted skylight for different cloud conditions. Our observations are supported by measurements of column liquid water path by multichannel microwave radiometry, cloud structure by millimeter cloud radar observations, and cloud base by a laser ceilometer. For the investigated multilayer cloud covers (decks of stratus, cumulus, altostratus, and cirrus), our measurements indicate that the photon path statistics are mostly governed by anomalous diffusion, whereby classical diffusion occurs in the limiting case of a single compact (plane parallel) cloud layer. The ratio for the inferred second and first moments of the path lengths confirms the relation recently derived by Davis and Marshak (2002) for photon diffusion in single optically thick cloud layers and extends it to more complex cloud geometry.