We have performed infrared spectroscopy of meteoritic calcium-aluminum-rich inclusions (CAIs) from the CV chondrites Leoville and Allende. While some previous studies have focused on the wavelength range l < 25 km, we aimed at a detection and identification of CAI bands at wavelengths from 6 to 75 km. The resulting spectra have been compared with laboratory mineral spectra of typical CAI constituents such as melilite (a solid solution of gehlenite Ca sub(2)Al sub(2)SiO sub(7) and akermanite Ca sub(2)MgSi sub(2)0 sub(7)), spinel (MgAl sub(2)O sub(4)), diopside (CaMgSi sub(2)O sub(6)), and its Al- and Ti-rich variety fassaite. Sixteen bands in a type-B1 Leoville CAI transmittance spectrum could be assigned to melilite and spinel, 13 bands in the spectrum of a B3 Allende CAI were assigned to Al-Ti-diopside (fassaite), spinel, and nepheline; both cases were in accordance with the sample's respective mineralogical and chemical composition. CaO (lime) is not detected spectroscopically in the CAI spectra, as it is (contrary to previous notions) not even a trace component in CAIs, at least in their present (partially reprocessed) state. The astrophysical relevance of our study lies in the fact that the main CAI minerals such as melilite, Al-Ti-diopside (fassaite), spinel, and anorthite are expected to be present in protoplanetary disks. Hence, the detection of Ca, Al-minerals in protoplanetary disks should only be a matter of increased instrumental sensitivity, or spatial and spectral resolution, and quality (e.g., wavelength coverage) of comparative laboratory spectra.