The charge-exchange method is now one of the main techniques for ion injection into accelerators and storage rings. The disadvantages of conventional methods, based on the atom or ion stripping in a material target, are emittance growth, energy straggling, and production of ions in many charge states. Recently suggested stripping methods based on direct photoionization require employment of hard-UV lasers, which still do not exist and must obviously be very bulky and expensive. An alternative method, suggested for injection of proton beams, employs excitation of the atom to 3p intermediate state with subsequent Lorentz ionization in a magnetic field gradient. This technique applies rigid requirements to laser characteristic and is not free of growing of the beam divergence. In this paper a variant of the stripping technique based on the resonantly enhanced two-photon ionization (RETPI) is considered. The technique allows ionization of singly charged ions of the elements from helium to bismuth. A variant of the technique can be used for proton injection. RETPI can be applied for both ion injection and stacking, as well as for diagnostics of ion beam characteristics on the orbit. Stripping efficiency can be about 100% for the singly charged ions having the singlet ground state and decreases for the other ions. Special methods for “cleaning” unwanted atomic states in such ions, that can provide high stripping efficiency, are discussed. Excimer lasers with very moderate parameters can be employed for implementation of this technique for almost all elements. Numerical examples show that for most of the singly charged ions and for hydrogen atom necessary laser-beam energy density is merely 0.5–8 J/cm^{2} for a 1 m interaction region, and is 10 times higher for several light ions.