Experimental cross sections are presented for single-and double-electron capture by C q+ , N q+ , and O q+ ͑q =2-6͒ ions from He at incident energies of ͑1.0-1800͒q eV. Measurements were performed by using a mini-electron-beam-ion-source apparatus in combination with an octopole-ion-beam-guide. The cross sections are found to vary significantly depending on the collision energy as well as on the projectile species. Some cross sections reveal minima at incident energies of a few eV/ u, below which the cross sections increase with decreasing incident energy. To account for the experimental results, we developed a formalism of velocitydependent capture cross sections within the framework of the classical over barrier model by employing an induced dipole interaction potential between the collision partners. In the calculations, doubly excited levels of projectile ions, formed via simultaneous excitation of the outermost projectile electron, were taken into consideration. It is found that the present model can satisfactorily reproduce the experimentally obtained energy dependence as well as absolute values of the cross sections. We conclude that the attractive induced dipole potential and simultaneous projectile excitation are important in low energy electron-capture collisions.