Mars is the only planet other than Earth in the Solar System that has a preserved nonpolar geological record of glaciation on its surface. Nonpolar ice deposits on Mars have been linked to variations in spin-axis obliquity that cause mobilization of polar ice and redeposition at lower latitudes, forming ice-rich and glacial deposits. Remnant nonpolar glacial deposits are found across the northern mid-latitudes where surface ice is not currently stable, implying that different climatic conditions existed on Mars in the past. Individual glacial deposits are often too small to date reliably using impact crater size-frequency data. We describe a novel approach that allows us to derive new information about when glaciation occurred in broad areas of the northern mid-latitudes. In this region we have classified (1) craters that superpose preexisting glacial deposits and were modified by later accumulation (and therefore formed during an epoch when glaciation was occurring), and (2) craters that are superposed on glacial deposits but are themselves unmodified by ice accumulation (and thus post-date significant glaciation). The sparse population of post-glacial craters reveals that the last period of extensive ice deposition of this type in this latitude band was recent (Late Amazonian). The substantial number of craters formed during the recurring glacial periods implies that northern mid-latitude glaciation was a long-lived recurring process, occurring over a period of at least ∼600 m.y. On the basis of Mars atmospheric general circulation models, these results are consistent with higher obliquity being common in the past, with recurring periods of obliquity exceeding the 25° axial tilt of Mars today. These observations support the statistical prediction of J. Laskar and colleagues that the median obliquity during the Amazonian was ∼35°–40°.