We present a theoretical analysis of high-order harmonic generation from ion-atom collisions in the presence of linearly polarized intense laser pulses. Photons with frequencies significantly higher than in standard atomic high-harmonic generation are emitted. These harmonics are due to two different mechanisms: (i) collisional electron capture and subsequent laser-driven transfer of an electron between projectile and target atom; (ii) reflection of a laser-driven electron from the projectile leading to recombination at the parent atom.PACS numbers: 42.65. Ky,34.50.Rk,32.80.Rm,34.70+e Over the last decades, a vast amount of work has been devoted to the study of ion-atom collisions [1] Kirchner [7] investigate fast collisions in the presence of a strong laser field. In Ref.[6], excitation mechanisms are discussed, while Ref. [7] focuses on ionization and electron capture. In both cases, the presence of the field leads to a significant modification of the collision process. On the other hand, there has been no study on the question how typical strong-field processes in atoms, such as high-order harmonic generation (HHG) [8] and above-threshold ionization [9], are modified due to the impact of an ion projectile. In HHG, a large number of incoming laser photons are converted into a single high-energy photon. HHG experiments are presently pursued with great effort [10,11] since the process serves as a source of coherent XUV radiation and attosecond pulses.In the present work, we investigate HHG in laserassisted ion-atom collision. We focus on impact velocities such that the time-scales of nuclear and electronic motion are comparable, i.e., we have significant probabilities for collisional electron transfer from the target to the projectile. For sufficiently long laser pulse durations, the laser-driven electron effectively sees a large range of internuclear distances during one laser pulse. When the laser polarization axis is parallel to the ion impact velocity, we show that this situation results in the generation of high harmonics with photon energies much higher than usually obtained in atomic HHG.The classical recollision model [12] describes atomic HHG as a sequence of strong-field ionization, acceleration of the electron in the laser field and recombination with the core. Within this model, the maximum return energy of the laser-driven electron is 3.17U p where2 ) is the ponderomotive potential for a laser with field amplitude E 0 and frequency ω. The maximum energy of the emitted photons is then equal to 3.17U p +I p where I p is the atomic ionization potential. For ion-atom collisions, we show below how the interplay between collisional electron capture and laser-driven electron transfer between target and projectile leads to new mechanisms of HHG with cutoffs at significantly higher energies.We consider collisions of protons on hydrogen atoms for proton energies of 2 keV (impact velocity v = 0.283 a.u.). Due to the large impact momentum, the projectile trajectory is assumed to be classical and along a s...