AbstractIn part 1Math. meth. in the Appl. Sci, 10, 125–144 (1988).we studied the principle of limiting absorption for local perturbations Ω of then‐dimensional domain Ω0= ℝn−1× (0, π). In this second part we extend our investigations to the time‐dependent theory and show that absence of admissible standing waves implies the validity of the principle of limiting amplitude for every frequency ω≥0 ifn≠ 3 and for ω ≠ 2, 3,… ifn= 3, respectively. In particular, the principle of limiting amplitude holds for every ω≥0 in the casen≠ 3 and for every ω ≠ 2, 3,… in the casen= 3 if Ω≠Ω0andν·x′ ⩽0 on ∂Ω, wherex′ = (x1,…,xn−1, 0) and ν is the normal unit vector on ∂Ω pointing into the complement of Ω This result stands in remarkable contrast to the fact that both principles are violated in the case of the unperturbed domain Ω0at the frequencies ω = 1, 2,… ifn⩽3. The question of the asymptotic behaviour of the solution ast→