As part of a large project to study the rate, distribution and history of star formation in the outer parts of galactic disks (Ferguson, PhD thesis), we have obtained very deep Hα and B-band images of the nearby face-on spiral NGC1058. Our images reveal extremely low surface brightness outer spiral arms in the B-band which extend well beyond the Holmberg radius and appear to be aligned with underlying HI spiral arms. These features contrast greatly to the flocculent appearance of the innermost regions of the disk and the complete absence of any well defined-arms in the Hα image. The surface brightness profile derived from the B-band image exhibits a sharp fall off in the inner regions of the disk followed by a much shallower decline beyond ~ R25 and consequently a single exponential disk cannot be fit to the entire profile.