  We study the Photon statistics in the superpositions of coherent states
$|\alpha\rangle$ and $|\alpha^*\rangle$ named ``Schr\"odinger real and
imaginary cat states''. The oscillatory character of photon distribution
function (PDF) emerging due to the quantum interference between the two
components is shown, and the phenomenon of the quadrature squeezing is observed
for the moderate values of $|\alpha|\sim 1$. Despite the quantity
${\langle\triangle n^2\rangle}/{\langle n\rangle}$ tends to the unit value
(like in the Poissonian PDF) at $|\alpha|\gg 1$, the photon statistics is
essentially non-Poissonian for all values of $|\alpha|$. The factorial moments
and cumulants of the PDF are calculated, and the oscillations of their ratio
are demonstrated.
