At room temperature, the ν(3) (1136 cm(-1)) absorption band of oxygen in silicon and Si(1 - x)Ge(x) alloys consists of dozens of components, masking the properties of the individual transitions. Here, experimental data are presented for the evolution of the ν(3) band in the temperature range 0 < T < 300 K and the composition range 0 ≤ x ≤ 0.066. The vibrational potential for Si:O is developed to provide accurate fits to the absorption data. The potential predicts properties consistent with published studies, including hydrostatic stress experiments. Extending the model to Si(1 - x)Ge(x) allows the properties of the alloy-induced O(i)-I, O(i)-II and O(i)-III components to be investigated accurately to higher values of x than hitherto. The properties of O(i)-I are understood as perturbations by Ge atoms of Si:O, and O(i)-III is rationalized in terms of off-axis movement of the O atom resulting from the nearby Ge atom. Challenges to theory are: the behaviour of O(i)-II, understanding the strain fields generated by Ge atoms in Si, and the reduced coupling of the ν(2) and ν(3) modes with increasing amplitude in the ν(2) mode.