Phonon dispersion relations and thermal conductance in AlxGa1−xAs alloy nanowires with varying compositions are investigated. When x varies from 0 to 1, the lowest-energy mode remains almost unchanged, while the cutoff frequency of the high-order modes increases. The thermal conductance of AlxGa1−xAs alloy nanowires is inversely proportional to the Al content x, but proportional to the nanowire width. For a two-terminal GaAs/AlxGa1−xAs/AlAs transport system, it is found that the thermal conductance first decreases and then increases as x increases from 0 to 1. The minimum thermal conductance at the critical x = 0.66 can be observed independent of the nanowire width. A concise analysis of these results is made.