Using the NIRSPEC spectrograph at Keck II , we have obtained echelle spectra covering the range 1.5 - 1.8 ~ { } \mu m for 2 of the brightest giants in Liller 1 and NGC 6553 , old metal rich globular clusters in the Galactic bulge . We use spectrum synthesis for the abundance analysis , and find [ Fe / H ] = -0.3 \pm 0.2 and [ O / H ] = +0.3 \pm 0.1 ( from the OH lines ) for the giants in both clusters . We measure strong lines for the alpha elements Mg , Ca , and Si , but the lower sensitivity of these lines to abundance permits us to only state a general [ \alpha / Fe ] = +0.3 \pm 0.2 dex . The composition of the clusters is similar to that of field stars in the bulge and is consistent with a scenario in which the clusters formed early , with rapid enrichment . We have difficulty achieving a good fit to the spectrum of NGC 6553 using either the low or the high values recently reported in the literature , unless unusually large , or no \alpha -element enhancements are adopted , respectively .