  FU Orionis (FUor) and EX Lupi (EXor) type objects are two groups of peculiar
and rare pre-main sequence low-mass stars that are undergoing powerful
accretion outbursts during their early stellar evolution. Water masers are
widespread in star forming regions and are powerful probes of mass accretion
and ejection, but little is known about the prevalence of them toward
FUors/EXors. We perform the first systematic search for the 22.2 GHz water
maser line in FUors/EXors to determine its overall incidence to perform
follow-up high angular resolution observations. We used the Effelsberg 100-m
radio telescope to observe the 22.2 GHz H2O maser toward a sample of 51
objects. We detect 5 water masers; 3 are associated with eruptive stars,
resulting in a 6% detection rate for eruptive sources. These detections include
one EXor, V512 Per (also known as SVS 13 or SVS 13A), and two FUors, Z CMa and
HH 354 IRS. This is the first reported detection of water maser emission
towards HH 354 IRS. We detect water maser emission in our pointing towards the
FUor binary RNO 1B/1C, which most likely originates from the nearby deeply
embedded source IRAS 00338+6312 (~4'', from RNO 1B/1C). Emission was also
detected from H$_2$O(B) (also known as SVS 13C), a Class 0 source ~30'', from
the EXor V512 Per. The peak flux density of H$_2$O(B) in our observations,
498.7 Jy, is the highest observed to date. In addition to the two non-eruptive
Class 0 sources (IRAS 00338+6312 and H$_2$O(B) /SVS 13C), we detect maser
emission towards one Class 0/I (HH 354 IRS) and two Class I (V512 Per and Z
CMa) eruptive stars. We demonstrate the presence of 22.2 GHz water maser
emission in FUor/EXor systems, opening the way to radio interferometric
observations to study these eruptive stars on small scales. Comparing our data
with historical observations suggest that multiple water maser flares have
occurred in both V512 Per and H$_2$O(B).
