  We obtain several generalizations the Hellinger theorem about $l^2$ solutions
of difference equations: instead of second order equations and $
l^2$-solutions, we consider second-order equations with matrix coefficients and
their solutions in $l^p,\; 1\le p\le \infty$. In particular it is shown that
for a certain class of symmetric difference equations an analog of this theorem
holds for $1\le p \le 2$, but it does not hold for $p>2$.
