  The SuperKamiokande collaboration has presented results on the observation of
solar neutrinos. The Sudbury Neutrino Observatory (SNO) is also expected to go
on-line in the near future. We propose several new variables, insensitive to
the absolute flux of the initial solar neutrino beam, which probe the shape of
the observed spectrum at these experiments and can sensitively signal neutrino
oscillations. One class of such variables involves normalised moments of the
distributions recorded at the two facilities while another variable, specific
to SNO, depends on the integrated charged and neutral current signals. The
utility of these variables in the context of supernova neutrinos, both from the
collapse epoch and the post-bounce era, is also emphasised. It is shown that,
notwithstanding the imprecise nature of the information about the initial
neutrino spectra from a supernova, oscillations can be detected using these
variables and it will be possible to distinguish between the alternatives of
oscillation to a sequential neutrino {\em vis-a-vis} that to a sterile
neutrino.
