Consider the neutral evolution equation d= ( ) ( ) ( , ),dt Fu B t u t t u t t + Φ under the conditions that thefamily of linear partial differential operators (B t ( ))t≥0 generates the evolutionary process(U t s ( , ))t s ≥ ≥0 having an exponential dichotomy on the half-line and the nonlinear delay operatorΦ ⋅ ( , ) t satisfes the ϕ -Lipschitz condition, where ϕ belongs to some admissible space on the halfline. The existence of admissibly stable manifolds of -class is obtained in Nguyen - Trinh [Taiwan.J. Math. 23 (2019), 897-923]. This short paper discusses the application of the theoretical result tostudy asymptotic behavior of a neutral version of the diffusive Hutchinson equation..