We have performed small-angle (SAXS) and wide-angle X-ray scattering (WAXS) measurements on the lamellar phase and on large unilamellar vesicles (LUVs) of DC(13)PC in the temperature range corresponding to the anomalous swelling regime of multibilayer systems, adjacent to the chain melting transition, and across the transition. Our SAXS measurements indicate that on cooling from the L(alpha) phase, a uniform progressive swelling of the lamellar system to anomalous distances, starting approximately 2 degrees C above the main transition, is followed by a region of coexistence, covering the width of the transition ( approximately 0.6 degrees C). Across the transition region, a progressively increasing volume fraction of gel phase with a constant P (beta') interlamellar distance coexists with a decreasing amount of nongel phase that keeps on swelling to longer distances. Along both the swelling and the transition regions, anomalies in the specific heat are observed revealing a two-step process. Simultaneous WAXS experiments show a progressive "density" increase along the swelling region, constituting a direct spectroscopic evidence of an "evolving membrane" approaching the transition in a bulk real system. Calorimetric and densitometric measurements on LUVs are also presented, together with WAXS results, that show the existence of a double step main transition in a single component nanosized closed bilayer.