Observation and analyses of the atmospheric pressure at the surface on Mars for several Martian years has led to the discovery of transient events in the daily pressure variations of an unusual nature. These events last only a few sols (Mars days), appear to repeat on an annual basis to within a few sols, appear to cover a large portion of the hemisphere on the same sol or at least within a few sols, occur in pairs with separations of 20 sols in some instances, are coincident with the annual pressure minimum (i.e., the maximum concentration of carbon dioxide in the southern hemisphere), and consist of spectral components near to, and sometimes identical in, frequency to the diurnal and semidiurnal harmonics. It is suggested that these events are Kelvin, normal-mode, transient, global oscillations. Examination of the initiation of the 1977A, 1977B, and 1982A global dust storms indicate that pseudo-diurnal and some-times pseudo-semidiurnal oscillations exist during the initiation phase and might be involved in triggering the global dust storms, possibly in conjunction with winds due to longer-period circulations. The diurnal harmonic disappears prior to the 1977B global dust storm and is replaced by an oscillation at 1.1 cycles/sol. If the lack of a classical diurnal tide indicates the suppression of convection, this might partially explain the slow growth of the 1977B storm. The daily average pressure during the transient season, which precedes the global dust storm season by almost one fourth of a year, exhibits a different behavior during the global dust storm years than during the nonglobal dust storm years. This implies that the global circulation must differ significantly in these cases and may be related to the presence or absence of global dust storms later in a given year. These analyses suggest that an almost diurnal and an almost semidiurnal, high-frequency global oscillation, different from the classical solar-driven tides, may be quite common on Mars.