In many areas of science and technology the ionization of the molecules that constitute the air by ion impact is of great relevance. In astrophysics, the ionization and dissociation of the air molecules by swift ions impact from cosmic radiation and the solar wind provokes different effects on atmosphere. In medical physics, the reference and relative dosimetry is performed using ionization chambers constituted by a cavity that contains air and an electrometer that determine the charge generated after the pass of the ionizing radiation. The measured values are converted to dose in liquid water by applying different correction factors and physical parameters such as the stopping power ratios air/water and the W-values (energy required to generate an ionic pair) [1]. The ionization processes are of relevance in the computation of these physical parameters for protontherapy and hadrontherapy (ion-beam cancer therapy). In a previous article, multiple ionization cross sections (MICS) of carbon monoxide, nitrogen and oxygen by proton impact were calculated using the Independent Electron Model (IEM), describing the molecules as two atoms at the equilibrium distance [2]. In the present work, MICS of air molecules by proton and heavy ion impact are calculated applying the IEM taking into account the molecular character of the target. The molecular orbitals are described using the CNDO (Complete Neglect of Differential Overlap) model [3]. An exponential model is used to represent the single particle ionization probabilities as a function of the impact parameter. The single ionization cross sections required are calculated by applying different theoretical models [3,4]. Auger-type emission is analysed, showing the importance of post-collisional contributions to the MICS at high impact energies. The results are in good agreement with experimental data.