A ring R is called right McCoy if whenever non-zero polynomials f (x) and g(x) in R[x] satisfy f (x)g(x) = 0, then f(x)r = 0 for some non-zero r ∈ R. A ring R is Armendariz if f(x)g(x) = 0 implies that all pairwise products of coefficients of f(x) and g(x) are zero. In my talk I am going to present some new results concerning above mentioned classes of rings. (This talk is based on joint work with Ryszard Mazurek.)