Nagumo's equation is a third order non-linear ordinary differential equation d 3 u d x 3 − c d 2 u d x 2 + f ′ ( u ) d u d x − ( b / c ) u = 0 where f ( u ) = u ( 1 − u ) ( u − α ) , 0 < α < 1 . In this paper we have developed a technique to determine those values of the parameters a , b and c which permit non-constant bounded solutions.