We present the stellar and gas kinematics of a sample of 18 nearby late-type spiral galaxies (Hubble types ranging from Sb to Sd), observed with the integral-field spectrograph SAURON at the 4.2-m William Herschel Telescope. SAURON covers the spectral range 4800-5380Å, allowing us to measure the Hβ, Fe, Mgb absorption features and the emission in the Hβ line and the [OIII]λλ4959, 5007Å and [NI]λλ5198, 5200Å doublets over a 33 × 41-arcsec2 field of view. The maps cover the nuclear region of these late-type galaxies and in all cases include the entire bulge. In many cases the stellar kinematics suggests the presence of a cold inner region, as visible from a central drop in the stellar velocity dispersion. The ionized gas is almost ubiquitous and behaves in a complicated fashion: the gas velocity fields often display more features than the stellar ones, including wiggles in the zero-velocity lines, irregular distributions, ring-like structures. The line ratio [OIII]/Hβ often takes on low values over most of the field, probably indicating a wide-spread star formation.