The magnetosheath is inherently complex and rich, exhibiting various kinds of structures and perturbations. It is important to understand how these structures propagate and evolve and how they relate to the perturbations. Here we investigate a kind of magnetosheath structure known as a magnetic dip (MD). As far as we are aware, there have been no previous studies concerning the evolution (contracting or expanding) of these types of structures, and their propagation properties cannot be unambiguously determined. In this study, using Magnetospheric MultiScale (MMS) high-temporal resolution data and multispacecraft analysis methods, we obtain the propagation and dynamic features of a set of MDs. Four different types of MDs are identified: "frozen-in," "expanding," "contracting," and "stable-propagating." Significantly, a stable-propagation event is observed with a sunward propagation component. This indicates that the source of the structure in this case is closely associated with the magnetopause, which provides strong support to the contention in earlier research. We further reveal the mechanism leading to the MD contraction or expansion. The motion of the MDs boundary is found closely related with the dynamic pressure. The scale of the contracting and expanding events are typically similar to 5-20 rho(i) (ion gyroradius), significantly smaller than that of frozen-in events (similar to 40 rho(i)). The observations could relate large-scale (more than several tens of rho(i)) and kinetic-scale (less than rho(i)) MDs, by revealing an evolution that spans these different scales, and help us better understand the variation and dynamics of magnetosheath structures and plasmas.