Mid-infrared observations (3.6 - 24 microns) of normal giant elliptical galaxies with the Spitzer space telescope are consistent with pure populations of very old stars with no evidence of younger stars. Most of the stars in giant elliptical galaxies are old but the mean stellar age determined from Balmer absorption in optical spectra can appear much younger due to a small admixture of younger stars. The mean stellar age can also be determined from the spectral energy distribution in the

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... rared which decreases with time relative to the optical emission and shifts to shorter wavelengths. The observed flux ratios F_8um/F_3.6um and F_24um/F_3.6um for elliptical galaxies with the oldest Balmer line ages are lower than predicted by recent models of single stellar populations. For ellipticals with the youngest Balmer line ages in our sample, 3-5 Gyrs, the flux ratios F_24um/F_3.6um are identical to those of the oldest stars. When theoretical mid-IR spectra of old (12 Gyr) and young stellar populations are combined, errors in the F_24um/F_3.6um observations are formally inconsistent with a mass fraction of young stars that exceeds ~1%. This is less than the fraction of young stars expected in discussions of recent surveys of elliptical galaxies at higher redshifts. However, this inconsistancy between Balmer line ages and those inferred from mid-IR observations must be regarded as provisional until more accurate observations and theoretical spectra become available. Finally, there is no evidence to date that central disks or patches of dust commonly visible in optical images of elliptical galaxies contribute sensibly to the mid-IR spectrum.