We have found that a rather simple thermal model of the Martian surface, in combination with current observations of the atmospheric composition, points strongly toward the conclusion that the polar caps of Mars consist almost entirely of frozen CO(2). This study was based upon the following principal assumptions. 1) Carbon dioxide is a major constituent of the Martian atmosphere. 2) The blanketing effect of the atmosphere is small, and due principally to the absorption band of CO(2) near 15 microns. 3) Lateral and convective heat transfer by the atmosphere is negligible. 4) The far-infrared emissivity of the Martian soil and of solid CO(2) are near unity. 5) The reflectivities of the soil and of solid CO(2) in the visible part of the spectrum are about 0.15 and 0.65, respectively. 6) Values for soil conductivity, density, and specific heat are those characteristic of powdered minerals at low gas pressure. 7) Water is a minor constituent of the Martian atmosphere, the maximum total amount in the atmosphere being 10 to 30 X 1O(-4) g cm(-2). In addition, several simplifications were made, which might have significant effects but should not alter our principal conclusions. Among these are the following. 1) Local blanketing or snowfall effects due to clouds or polar haze were ignored. 2) Dark and light areas were not differentiated in this study, although Sinton and Strong (6) have observed temperature differences between such areas. 3) The effects of local topography and microrelief were neglected. We believe that these must have quite significant effects at the higher latitudes, especially in connection with the evaporation of the remanent south polar cap. 4) Variation of reflectivity with angle of incidence of the sunlight was neglected. 5) Temperature dependence of soil conductivity and specific heat was ignored. 6) Effects of saturation of the soil by ice upon the thermal properties of the soil were neglected. Although in our main investigation we used certain specific values for the various relevant parameters, we also tested the effects of moderate changes in these quantities. Specifically, the soil conductivity was varied by a factor of 3, the albedo and emissivity of the surface were changed by 15 to 20 percent, and the effects of a gross amount of atmospheric blanketing were studied, as described. Only the last of these variations had any significant effect on the model, and other results of the atmospheric blanketing were in disagreement with other physical observations of the planet. Consequently, we find it difficult to avoid the conclusion that CO(2) must condense in large amounts relative to H(2)0. The main conclusions indicated by this study are the following. 1) The atmosphere and frost caps of Mars represent a single system with CO(2) as the only active phase. 2) The appearance and disappearance of the polar caps are adequately explained on the presumption that they are composed almost entirely of solid CO(2) with perhaps an occasional thin coating of water ice. 3) If the currently reported water-vapor observations are correct, water-ice permafrost probably exists under large regions of the planet at polar and temperate latitudes. 4) The geochemically anomalous enrichment of CO(2) relative to N(2) in the present Martian atmosphere may be a result of selective trapping of CO(2) in the solid phase at and under the surface. 5) If the basic evaporation and condensation mechanisms for CO(2) and H(2)O discussed in this article are correct, the possible migration of volatile organic compounds away from the warm temperate regions of the planet and their possible accumulation in the polar regions need to be carefully considered.