The author studies the oscillatory behavior of solutions of the nonlinear difference equation \[ \Delta^m u(n)=f(n,u(n),\dots,\Delta^{m-1} u(n)), m\geq 2. \] The obtained results are the discrete analogues of the well known oscillation theorems for differential equations due to I. T. Kiguradze [Differ. Uravn. 10, 1387-1399 (1974; Zbl 0304.34033)].