Existence and global attractivity of periodic solutions to some subclasses of the following class of difference equations x n+1 = q n x n + f (n, x n , x n−1 ,. .. , x n−k), n ∈ N 0 , where k ∈ N 0 , (q n) n∈N 0 is a T-periodic sequence (T ∈ N), and f : N 0 × R k+1 → R is a T-periodic function in the first variable, which for each n ∈ {0, 1,. .. , T − 1} is continuous in other variables, are studied,