Some nonoscillation criteria are obtained for second order quasilinear differential equations of the form (E) [r(t)\u'(t)\(p-2)u'(t)]' + c(t)\u(t)\(p-2)u(t) = 0, where p > 1, r(t) is an element of C-1 ([t(0), infinity); (0, infinity)) and c(t) is an element of C([to, infinity); R). These results extend some nonoscillation criteria of Hille, Wintner, Potter, Moore, Willett for the equation [r(t)u'(t)]' + c(t)u(t) = 0 to equation (E).
