  We present a spectroscopic analysis of the metallicities, ages, and
alpha-elements of the globular clusters (GCs) in the giant elliptical galaxy
(gE) NGC 4636 in the Virgo cluster. Line indices of the GCs are measured from
the integrated spectra obtained with Faint Object Camera and Spectrograph
(FOCAS) on the Subaru 8.2 m telescope. We derive [Fe/H] values of 59 GCs based
on the Brodie & Huchra method, and [Z/H], age, and [a/Fe] values of 33 GCs from
the comparison of the Lick line indices with single stellar population models.
The metallicity distribution of NGC 4636 GCs shows a hint of a bimodality with
two peaks at [Fe/H]=-1.23 (sigma=0.32) and -0.35 (sigma=0.19). The age spread
is large from 2 Gyr to 15 Gyr and the fraction of young GCs with age < 5 Gyr is
about 27%. The [a/Fe] of the GCs shows a broad distribution with a mean value
[a/Fe]~0.14 dex. The dependence of these chemical properties on the
galactocentric radius is weak. We also derive the metallicities, ages, and
[a/Fe] values for the GCs in other nearby gEs (M87, M49, M60, NGC 5128, NGC
1399, and NGC 1407) from the line index data in the literature using the same
methods as used for NGC 4636 GCs. The metallicity distribution of GCs in the
combined sample of seven gEs including NGC 4636 is found to be bimodal,
supported by the KMM test with a significance level of >99.9%. All these gEs
harbor some young GCs with ages less than 5 Gyr. The mean age of the metal-rich
GCs ([Fe/H] > -0.9) is about 3 Gyr younger than that of the metal-poor GCs. The
mean value of [a/Fe] of the gE GCs is smaller than that of the Milky Way GCs.
We discuss these results in the context of GC formation in gEs.
