Summary: We establish some new criteria for the oscillation of the even order neutral dynamic equation \[ \left( a(t)\left( \left( x(t)-p(t)x(\tau (t))\right) ^{\Delta^{n-1}}\right) ^{\alpha}\right) ^{\Delta}+q(t)\left( x^{\sigma}(g(t))\right) ^{\lambda}=0 \] on a time scale \(\mathbb{T}\), where \(n \geq 2\) is even, \(\alpha \) and \(\lambda \) are ratios of odd positive integers, \(a\), \(p\) and \(q\) are real valued positive rd-continuous functions defined on \(\mathbb{T}\), and \(g\) and \(\tau \) are real valued rd-continuous functions on \(\mathbb{T}\). Examples illustrating the results are included.