We employ Kranoselskii's fixed point theorem to establish the existence of nonoscillatory solutions to the second-order neutral delay dynamic equation [ x ( t ) + p ( t ) x ( τ 0 ( t ) ) ] Δ Δ + q 1 ( t ) x ( τ 1 ( t ) ) − q 2 ( t ) x ( τ 2 ( t ) ) = e ( t ) on a time scale 𝕋. To dwell upon the importance of our results, one interesting example is also included.