  Intrigued by recent high-energy study results for nearby galaxies with
gamma-ray emission and in particular NGC~1068 that has been detected as a
neutrino-emitting source by the IceCube Neutrino Observatory, we conduct
detailed analysis of the $\gamma$-ray data for the galaxies NGC~1068 and
NGC~253, obtained with the Large Area Telescope onboard {\it the Fermi
Gamma-ray Space Telescope}. By checking for their possible spectral features
and then constructing light curves in corresponding energy ranges, we identify
spectral-change activity from NGC ~1068 in $\geq$2\,GeV energy range and
long-term detection significance changes for NGC~253 in $\geq$5\,GeV energy
range. In the former, the emission appears harder in two half-year time periods
than that in the otherwise `quiescent' state. In the latter, a $\sim$2-times
detection significance decrease after MJD~57023 is clearly revealed by the
test-statistic maps we obtain. Considering studies carried out and models
proposed for the $\gamma$-ray emissions of the two sources, we discuss the
implications of our findings. We suspect that the jet (or outflow) in NGC~1068
might contribute to the \gr\ emission. The nature of the long-term detection
significance change for NGC~253 is not clear, but since the part of the GeV
emission may be connected to the very-high-energy (VHE) emission from the
center of the galaxy, it could be further probed with VHE observations.
