The models of glaciation and thawing of the outer surface of an offshore gas pipeline are presented. In the glaciation model the modification of Stefan condition is proposed which allows accounting for the special features of a sea ice growing in salt water. The algorithm of numerical solution to unsteady problem of glaciation (thawing) of the multilayer cylindrical area by the explicit front tracking method and some numerical simulation results of different variants of these problems, which are of practical interest, are given. The quantitative estimates of a shift to a quasi-stationary version of the glaciation (thawing) model of multilayer areas are obtained. The qualitative condition for the admissibility of using a quasi-stationary approximation for numerical simulation of glaciation of the multilayer area is found. These estimates are very important for the developing effective numerical algorithms for simulation of the unsteady regimes of gas transportation through the offshore gas pipelines. For the problems of thawing of the outer surface pipelines the equation is proposed, which allows finding the minimal ice layer thickness under researched conditions