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Let T ⊂ R be a periodic time scale in shifts ƍ±. We use a fixed point theorem due to Krasnosel'skiĭ to show that nonlinear delay in dynamic equations of the form x△(t) = -a(t)xσ (t) + b(t)x△(ƍ-(k, t))ƍ- △ (k, t) + q(t, x(t), x(ƍ-(k, t))), t ∈ T, has a periodic solution in shifts ƍ±.We extend and unify periodic differential, difference, h-difference, and q-difference equations and more by a new periodicity concept on time scales. [ABSTRACT FROM AUTHOR]