Techniques of coarse and fine analysis, based on curves of growth, were used to derive abundances in the atmospheres of HD 2665 and HD 6755, two metal-deficient stars of extremely high velocity. Abundances were compared with those in the Sun, using Conti's models for normal and metal-deficient K-giants; the ions, for normal abundances, were found to have a higher exictation temperature than the neutral atoms, but this difference disappears in the metal-deficient stars. In a small temperature interval, the relation between the model parameters 0eff and log g was determined in such a way that the total abundances derived from the neutral atoms were the same as those derived from the ions. Iron, chromium, titanium, and vanadium were used for that purpose and gave consistent results. The chief source of error in the final abundances is the effective temperature. If we adopt Oeff = 0.97, log g = 2.8, for HD 6755 and Oeff = 1.055, log g = 1.8, for HD 2665, then the deficiencies of iron relative to the Sun are by factors of 11 and 37, respectively. In HD 6755 all elements are equally deficient within a factor of 2, perhaps with the exception of europium. In HD 2665 the heavy s-process elements show a deficiency with respect to iron of about a factor of 3. For the elements C, N, and 0 a factor of 2 or 3 additional deficiency roughly fits the observations. The result for carbon is uncertain, in addition, because of the unknown oxygen carbon ratio. The turbulent velocities, from the curves of growth, are low: 0.7 km/sec for HD 6755 and 0 6 km/sec for HD 2665. Both stars move in retrograde orbits, with large W velocities, HD 2665 toward the galactic center and HD 6755 outward. Adopting 1 solar mass for the latter star, we find that it moves in a hyperbolic orbit. If 0.5 solar mass is adopted, the star will not escape from the Galaxy.