  We present the calculation of the virtual- and bremsstrahlung corrections of
O(alpha_s) to the matrix elements <d l+ l-|O_i|b>. This is the missing piece in
the NNLL results for various observables associated with the process B-> X_d l+
l-, like the branching ratio, the CP-rate asymmetry and the forward-backward
asymmetry. This paper is an extension of analogous calculations done by some of
us for the process B-> X_s l+ l-. As the contributions of the diagrams induced
by the operators O_1^u and O_2^u with a u-quark running in the quark loop are
strongly CKM suppressed, they were omitted in the analysis of B->X_s l+ l-.
This is no longer possible for B-> X_d l+ l-, as the corresponding
contributions are not suppressed. The main new work therefore consists of
calculating the O(alpha_s) corrections to <d l+ l-|O_{1,2}^u|b>. In this paper
we restrict ourselves to the range 0.05 < s/m_b^2 < 0.25 (s is the invariant
mass of the lepton pair), which lies above the rho- and omega-resonances and
below the J/psi-resonance. We present the analytic results for the mentioned
observables related to the process B-> X_d l+ l- as expansions in the small
parameters s/m_b^2, z = m_c^2/m_b^2 and s/(4 m_c^2). In the phenomenological
analysis at the end of the paper we discuss the impact of the NNLL corrections
on the observables mentioned above.
