Using the NIRSPEC spectrograph at Keck II, we have obtained infrared echelle spectra covering the 1.5-1.8 mu m range for giant stars in the massive bulge globular Clusters NGC 6440 and NGC 6441. We report the first high-dispersion abundance for NGC 6440, [Fe/H] = -0.56 +/- 0.02 and we find [Fe/H] = -0.50 +/- 0.02 for the blue Horizontal Branch cluster NGC 6441. We measure an average alpha-enhancernent of approximate to +0.3 dex in both Clusters, consistent with previous measurements of other metal rich bulge clusters, and favouring the scenario of a rapid-bulge formation and chemical enrichment. We also measure very low C-12/C-13 isotopic ratios (approximate to 5 +/- 1), suggesting that extra-mixing mechanisms are at work during evolution along the Red Giant Branch also in the high-nietallicity regime. We also measure Al abundances, finding average [Al/Fe] = 0.45 +/- 0.02 and [Al/Fe] = 0.52 +/- 0.02 in NGC 6440 and 6441, respectively, and some Mg-Al anticorrelation in NGC 6441. We also measure radial velocities nu(r) = -76 +/- 3 and nu(r) = +14 +/- 3 kms(-1) and velocity dispersions sigma = 9 +/- 2 and sigma = 10 +/- 2 kms(-1) in NGC 6440 and 6441, respectively.