Using the group crossing time t_c_ as an age indicator for galaxy groups, we have investigated the correlation between t_c_ and the group spiral fraction, as well as between t_c_ and the neutral hydrogen gas fraction of galaxy groups. Our galaxy group sample is selected from the SDSS DR7 catalog, and the group spiral fraction is derived from the Galaxy Zoo morphological data set. We found that the group spiral galaxy fraction is correlated with the group crossing time. We further cross-matched the latest released ALFALFA 70% H I source catalog with the SDSS group catalog and have identified 172 groups from the SDSS survey whose total H I mass can be derived by summing up the H I mass of all the H I sources within the group radius. For the galaxies not detected in ALFALFA, we estimate their H I masses based on the galaxies' optical colors and magnitudes. Our sample groups contain more than eight member galaxies, they cover a wide range of halo masses and are distributed in different cosmic environments. We derived the group H I mass fraction, which is the ratio of group H I mass to the group virial mass. We found a correlation between the H I mass fraction and the group crossing time. Our results suggest that long timescale mechanisms such as starvation seem to play a more important role than short timescale processes like stripping in depleting H I gas in the SDSS galaxy groups.