By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations ( p ( t ) ( x Δ ( t ) ) γ ) Δ + q ( t ) f ( x ( τ ( t ) ) ) = 0 on a time scale T , here γ ≥ 1 is a quotient of odd positive integers with p and q real-valued positive rd-continuous functions defined on T .