The concept of nil-symmetric rings has been introduced as a generalization of symmetric rings and a particular case of nil-semicommutative rings. A ringRis called right (left) nil-symmetric if, fora,b,c∈R, wherea,bare nilpotent elements,abc=0 (cab=0)impliesacb=0. A ring is called nil-symmetric if it is both right and left nil-symmetric. It has been shown that the polynomial ring over a nil-symmetric ring may not be a right or a left nil-symmetric ring. Further, it is also proved that ifRis right (left) nil-symmetric, then the polynomial ringR[x]is a nil-Armendariz ring.