Abstract： In this paper, we discuss the existence and multiplicity results of solutions to the following nonlinear fourth-order Neumann boundary value problem with parameters:{u(4)(t) + ηu"(t) - ξu(t) = λf(t, u(t)), t ∈ [0, 1], (1.1*)u'(0) = u'(1) = u"'(0) = u"' (1) = 0,where f: [0, 1] × R → R is continuous, ξ, η∈ R and λ∈ R+ are parameters, which satisfy the condition:ξ/π4+η/π2＜1, ξ≥-η2/4, η＜2π2.