We consider the equation ( r ( t ) ( y Δ ( t ) ) γ ) Δ + f ( t , x ( δ ( t ) ) ) = 0 , t ∈ T , where y ( t ) = x ( t ) + p ( t ) x ( τ ( t ) ) and γ is a quotient of positive odd integers. We present some sufficient conditions for neutral delay and mixed-type dynamic equations to be oscillatory, depending on deviating arguments τ ( t ) and δ ( t ) , t ∈ T .