We consider the process of electron-ion recombination in a powerful laser f
ield and investigate the spectrum of emitted x-ray radiation. This process
is of interest in the interaction of laser radiation with gaseous or solid
targets in connection with harmonic and coherent x-ray production. The proc
ess is treated in the framework of the inverse Keldysh-Faisal-Reiss model d
escribing the ingoing electron either by a Gordon-Volkov wave or by a Coulo
mb-Volkov solution. Even for higher energies of the impinging electrons, co
nsiderable Coulomb effects are recognized. We evaluate the rates of the gen
erated x-ray field and determine the energy range of its spectrum. The maxi
mum photon energy achieved by this process is estimated by (h) over bar ome
ga(X)=E-p + U-p + \E-B\ +2 root 2U(p)E(p), with E-p being the kinetic energ
y of the ingoing electron, U-p the ponderomotive energy, and E-B the bindin
g energy. The equivalence of the two models for the zero-range interaction
is also shown.