Recently an efficient method (DACG) for the partial solution of the symmetric generalized eigenproblem Ax = Ξ»Bx has been developed, based on the conjugate gradient (CG) minimization of the Rayleigh quotient over successive deflated subspaces of decreasing size. The present paper provides a numerical analysis of the asymptotic convergence rate Ο j of DACG in the calculation of the eigenpair Ξ» j , u j , when the scheme is preconditioned with A -1 . It is shown that, when the search direction are A-conjugate, Ο j is well approximated by 4/ΞΎ j , where ΞΎ j is the Hessian condition number of a Rayleigh quotient defined in appropriate oblique complements of the space spanned by the leftmost eigenvectors u 1 , u 2 , . . ., u j-1 already calculated. It is also shown that 1/ΞΎ j is equal to the relative separation between the eigenvalue Ξ» j currently sought and the next higher one Ξ» j +1 . A modification of DACG (MDACG) is studied, which involves a new set of CG search directions which are made M-conjugate, with M a matrix approximating the Hessian. By distinction, MDACG has an asymptotic rate of convergence which appears to be inversely proportional to the square root of ΞΎ j , in complete agreement with the theoretical results known for the CG solution to linear systems.