We present results from three multidecadal sensitivity experiments with time-varying solar cycle and quasi-biennial oscillation (QBO) forcings using National Center for Atmospheric Research's Whole Atmosphere Community Climate Model (WACCM3.1). The model experiments are unique compared to earlier studies as they use time-varying forcings for the solar cycle only and the QBO, both individually and combined. The results show that the annual mean solar response in the tropical upper stratosphere is independent of the presence of the QBO. The response in the middle to lower stratosphere differs depending on the presence of the QBO and the solar cycle but is statistically indistinguishable in the three experiments. The seasonal evolution of the solar and the combined solar-QBO signals reveals a reasonable agreement with observations only for the experiment in which both the solar cycle and the QBO forcing are present, suggesting that both forcings are important to generate the observed response. More stratospheric warmings occur during solar maximum and QBO west conditions. This appears to be the result of a QBO modulation of the background zonal mean wind climatology, which modifies the solar signal. Depending on the background wind, the small initial early winter solar signal in the subtropical upper stratosphere/lower mesosphere is enhanced during QBO east and diminished during QBO west conditions. This consequently influences the transfer of the solar-QBO signal during winter and results in the observed differences during late winter.