The paper studies non-Lie symmetry of the Klein-Gordon-Fock equation (KGF) in
$(p+q)$-dimensional Minkowsky space. Full set of symmetry operators for the
$n$-order KGF equation was explicitly calculated for arbitrary $n<\infty$ and
$p+q \leq 4$.
Definition was given for generalized Killing tensors of rank $j$ and order
$s$, and for generalized conformal Killing tensors of rank $j$ and order $s$ as
a complete set of linearly independent solutions of some overdetermined systems
of PDE. These tensors were found in explicit form for arbitrary fixed $j$ and
$s$ in Minkowsky space of dimension $p+q \leq 4$. The received results can be
used in investigation of higher symmetries of a wide class of systems of
partial differential equations.