Properties of radiative transitions from exciton states in a linear chain and in a ring (periodic boundary conditions) are examined. The two models exhibit a persistent difference in the radiation rate even for stationary-state transitions. Exciton wave packets are shown to radiate weakly if they originate at the end of the linear chain, strongly if they originate near the middle of the chain. The latter radiation shows also a strong periodic component. The radiation rate of a wave packet from a ring turns out to be the same as the rate from an isolated monomer and has no periodic components. For both the ring and the chain the wave packet is much more stable against decay than a stationary state. Radiation from a wave packet shows little deviation from the Breit—Wigner shape.