Hyperoxia or hypercapnia provides a useful experimental tool to systematically alter the blood oxygenation level dependent (BOLD) contrast. Typical applications include calibrated functional magnetic resonance imaging (fMRI), BOLD sensitivity mapping, vessel size imaging or cerebrovascular reactivity mapping. This article describes a novel biophysical model of hyperoxic and hypercapnic BOLD contrast, which accounts for the magnetic susceptibility effects of molecular oxygen that is dissolved in blood and tissue, in addition to the well-established effects caused by the paramagnetic properties of deoxyhaemoglobin. Furthermore, the concept of vascular component analysis (VCA) is introduced and is shown to provide a computationally efficient tool for investigating the vascular specificity of hyperoxic and hypercapnic BOLD contrast. A theoretical investigation of gradient and spin echo BOLD contrast based on computer simulations was performed to compare three different conditions (hypercapnia induced by breathing 6% CO2, hyperoxia induced by breathing 100% O2, and simultaneous hypercapnia and hyperoxia induced by breathing carbogen, i.e. 5% CO2 in 95% CO2) with baseline (breathing air). Simulations were carried out for different levels of metabolic oxygen extraction fraction (OEF) ranging from 0 to 0.5. The key findings can be summarised as follows: (i) for hyperoxia the susceptibility of dissolved O2 may lead to a significant arterial BOLD contrast; (ii) under normoxic conditions the susceptibility of dissolved O2 is negligible; (iii) an almost complete loss of BOLD sensitivity may occur at lower OEF values in all parts of the vascular tree, whereas hyperoxic BOLD sensitivity is largely maintained; (iv) under hyperoxic conditions, a transition from positive to negative BOLD contrast occurs with decreasing OEF values. These findings have important implications for experimental applications of hyperoxic and hypercapnic BOLD contrast and may enable new clinical applications in ischemic stroke and other forms of acquired brain injury.