Summary: Oscillatory and asymptotic properties of solutions of a class of nonlinear fourth order neutral dynamic equations of the form \[ (r(t)(y(t)+p(t)y(\alpha(t)))^{\Delta^2})^{\Delta^2}+ q(t)G(y(\beta(t)))=0\tag{H} \] and \[ (r(t)(y(t)+p(t)y(\alpha(t)))^{\Delta^2})^{\Delta^2}+ q(t)G(y(\beta(t)))=f(t)\tag{NH} \] for \(t\in[t_0,\infty]_\mathbb{T}\), \(t_0\geq 0\), where \(\mathbb{T}\) is a time scale such that \(\sup\mathbb{T}=\infty\), \(t_0\in\mathbb{T}\) are studied under the assumption \(\int^\infty_{t_0}\frac{t}{r(t)}\Delta t=\infty\) for various ranges of \(p(t)\). Sufficient conditions are obtained for the existence of bounded positive solutions of (NH) by using Schauder’s fixed point theorem.