In this paper, we establish the existence of nonoscillatory solutions to neutral dynamic equations with positive and negative coefficients on time scales of the form (x(t) − b a p(t, τ)x((t, τ))∆τ) ∆ + l i=1 r i (t)x(δ i (t)) − m j=1 s j (t)x(η j (t)) = 0. Two examples are included to illustrate our presented results. In our approaches, a key role is played by the fixed point technique.