The effect of long-term (11-year solar cycle) solar UV variability on stratospheric chemical and thermal structure has been studied using a time-dependent one-dimensional model. Previous studies have suggested substantial variations in local and total ozone, and in stratospheric thermal structure from solar minimum to solar maximum. It is shown here that significant variations also occur in some of the trace constituents. Members of the HO x family and N2O exhibit the largest variations, and these changes, if detected, may provide additional means of verifying the presence of solar UV variability and its effects. Some of the species show large phase differences with the assumed solar flux variation. The role of chemical and transport time constants on the time variations of the trace species is examined. Comparisons with reported ozone and temperature data show reasonable agreement for the period 1960 to 1972.