A formalism is developed for computing tidal variations in thermospheric composition and is used to investigate diurnal and semidiurnal variations in O, O2, N2, Ar, He, and H at minimum and maximum levels of sunspot activity. The model formally accounts for tidal temperatures, horizontal and vertical tidal winds, photochemistry and ion chemistry, thermal diffusion, and exospheric transport in determining the tidal variations of these constituents, as well as deviations from diffusive equilibrium in the time average component due to photochemistry, Jeans escape, or background vertical winds. A procedure is described for using available measurements to calibrate the diurnal and semidiurnal wind and temperature fields, which are used as inputs to model. Sunspot minimum calculations show excellent agreement with equatorial San Marco 3 Nace measurements in both amplitude and phase for diurnal and semidiurnal variations between 220 and 280 km. Major exceptions are the equatorial diurnal amplitude of Ar, which the model overestimates by 35%, and the equatorial diurnal amplitude of He, which the model underestimates by about 25%. Simulations for sunspot maximum conditions demonstrate substantial solar cycle differences in the vertical structures of amplitude and phase for each constituent and in the relative contribution of semidiurnal and diurnal components at different latitudes and heights. Consequently, a clear need is indicated for continued satellite mass spectrometer and accelerometer measurements over different levels of solar activity if comprehensive empirical models of thermosphere tides are to be developed.