We show that if f is a transcendental meromorphic function with a finite number of poles and f has a cycle of Baker domains of period p, then there exist C > 1 and r0 > 0 such { z : 1 C r < |z| < Cr } sing(f−p) ∅, for r r0. We also give examples to show that this result fails for transcendental meromorphic functions with infinitely many poles.
