The flow of marine atmospheric boundary layer (MABL) air across ocean-surface temperature fronts subjects the MABL to an abrupt change in surface thermal forcing. The MABL responds to this variable forcing by a readjustment of both the MABL heat and moisture content as well as the MABL depth. This note addresses questions raised in recent publications in this journal with a rigorous theoretical analysis for the simplest case, an equilibrated MABL crossing a very abrupt front at right angles. The MABL's adjustment is found by a solution to the mixed-layer budget of buoyancy and the entrainment closure based on the turbulent energetics of the MABL. Since the solution is analytic, this sample case can be easily extended to circumstances of more realistic forcing. The solution discussed here establishes a firm theoretical basis for previous, partly heuristic and partly empirical, work; highlights weaknesses of that approach, and shows how simplistic engineering solutions to complex geophysical problems can be completely misleading. ¿ American Geophysical Union 1987