  We have carried out a multi-epoch simultaneous survey of 22 GHz H$_2$O and 44
GHz Class I CH$_3$OH masers toward 103 ultracompact HII regions (UCHIIs)
between 2010 and 2017. We detected H$_2$O and CH$_3$OH maser emission in 74
(72%) and 55 (53%) UCHIIs, respectively. Among them, 3 H$_2$O and 27 CH$_3$OH
maser sources are new detections. These high detection rates suggest that the
occurrence periods of both maser species are significantly overlapped with the
UCHII phase of massive star formation. The CH$_3$OH maser lines always have
small (< 10 km s$^{-1}$) relative velocities with respect to the natal
molecular cores, while H$_2$O maser lines often show larger relative
velocities. Twenty four H$_2$O maser-detected sources have maser lines at
relative velocities > 30 km s$^{-1}$, and thirteen of them show extremely
high-velocity (> 50 km s$^{-1}$) components. The appearance and disappearance
of H$_2$O maser lines are quite frequent over six-month or one-year time
intervals. In contrast, CH$_3$OH maser lines usually do not exhibit significant
variations in the line intensity, velocity, or shape for the same periods. The
isotropic luminosities of both masers appear to correlate with the bolometric
luminosities of the central stars. This correlation becomes much stronger in
the case that data points in the low- and intermediate-mass regimes are added.
The maser luminosities also tend to increase with the radio continuum
luminosities of UCHIIs and the submillimeter continuum luminosities of the
associated dense cores.
