The asymptotic and oscillatory behavior of solutions of some general second-order nonlinear difference equations of the form
δ(anh(yn+1)δyn)+pnδyn+qn+1f(yσ(n+1))=0 nZ,
is studied. Oscillation criteria for their solutions, when “pn” is of constant sign, are established. Results are also presented for the damped-forced equation
δ(anh(yn+1)δyn)+pnδyn+qn+1f(yσ(n+1))=ennZ.
Examples are inserted in the text for illustrative purposes.