The orthodox view of vertebrate evolution holds that air-breathing first arose in gnathostome fishes inhabiting freshwater swamps and marshes of the Paleozoic Era (Barrell, 1916; Inger, 1957; Romer, 1966, 1967; Thomson, 1969a, 1971). Paleoclimatic evidence indicates that these aquatic environments were characterized by low levels of dissolved oxygen, at least during dry seasons, owing to the combined effects of high ambient temperature, inadequate circulation of the shallow waters by wind, and high oxygen demands of microbes and decaying vegetation (Barrell, 1916; Inger, 1957; Thomson, 1969a). In such environments, the habit of air-breathing presumably was subjected to strong selection pressures (Romer 1966, 1967; Thomson, 1971), for in the absenc,e of some auxiliary respiratory mechanism permitting the exploitation of atmospheric reservoirs of oxygen, survival seems to have been unlikely (Romer, 1966). Lungs subsequently evolved in the successful inhabitants of these stagnant waters as greater and greater reliance was placed upon air-breathing to provide the oxygen necessary to support metabolism. The strongest support for the aforementioned theory comes from consideration of the distribution of contemporary airbreathing fishes. T'hese fishes reach their highest diversity in warm, shallow inland waters of the tropical lowlands (Carter, 1957; Johansen, 1970), where hypoxic conditions commonly occur (Carter and Beadle, 1931; Willmner, 1934). Since the success of these swamp-dwelling fishes is related to their ability to tap atmospheric supplies of oxygen, it seems reasonable to conclude that comparable environmental conditions during the Paleozoic must have led to the evolution of air-breathing among ancient fishes (Carter and Beadle, 1931). Moreover, the air-breathing habit is quite uncommon among contemporary fishes inhabiting, marine or estuarine environments (Carter, 1957; Johansen, 1970). Since seawater generally is well circulated and fully aerated it is regarded as unlikely that Paleozoic fishes inhabiting this medium, like Recent fishes, could have met with difficulty in satisfying their needs for oxygen (Carter, 1957; Johansen, 1970). The theory for a freshwater origin of air-breathing (and lungs) in Paleozoic vertebrates has won wide acceptance; and the pervasiveness of the theory is revealed by the fact that certain groups of vertebrates are regarded as having originated in freshwaters, despite the existence of paleontologic evidence to the contrary, largely because they possess lungs (Thomson, 1969a,b). My objective is to show that necessary conditions for the evolution of air-breathing could have existed during the Paleozoic Era in certain marine or estuarine situations; and in this way I hope to provide for a re-interpretation of many of the paleontologic data.