The Talbot effect is investigated for oblique angles of illumination. From the transfer function of free space assuming small diffraction angles we calculate the self-imaging condition for periodic diffractive elements. Additionally, aberrations are considered, which are of third order in spatial frequency. These aberrations originate from the asymmetric off-axis configuration and cause distortions of the self-images. We include experimental verifications of our considerations and suggest applications of the off-axis Talbot effect to planar optics.