Control of breathing and gas exchange has been extensively investigated in unimodal animals, particularly mammals, in which ventilation is characteristically a regular and continuous process and gas exchange approximates to a steady-state system. Both static and dynamic models have been developed in control-theory analyses. Similar analyses are possible in unimodal fish, though few have been carried out. Control in bimodal animals, such as air-breathing fish and amphibians, is more difficult to understand and model. The evolutionary change from water to air breathing in vertebrates involves not only the adjustment of many control processes but also the development, in the early stages, of non steady states in gas exchangers, blood, and tissues. A simple control-system model, differing from mammalian counterparts in its greater emphasis on storage functions and its intermittently activated controller, is described for two suggested stages in the evolution of air breathing. The first of these stages is air gulping, in which a fixed and rather brief pattern of air breathing is activated by internal signals generated as a result of the inadequacy of the gills to provide sufficient oxygen for tissue metabolism. The second stage is that of burst breathing, in which lung ventilation is both begun and ended by internal signals so that burst duration is variable. The effects of adjusting parameters on variables of evolutionary importance, such as dive duration, burst duration, store renewal, and metabolic rate, can be examined in these two versions of the model. Refinements to incorporate arterial and venous compartments in the circulatory system, the shunting of venous and arterial blood streams in the heart, realistic oxygen dissociation curves, controller inputs from a wider range of sources, and the capacity to respond to some conditions with changes in ventilation rate as well as in burst and dive durations, are being developed. They should make the complex, non-steady-state interactions between gas exchangers, circulating blood, and tissues easier to understand and indicate the likely steps toward the evolution of steady-state systems seen in birds and mammals.