A "two-phase" continuum model of a developing tissue is formulated and some limiting cases are analyzed. In this "raisin-pudding" model, exchange occurs between cytoplasm and the immobilized cell organelles, and transport within the cytoplasm is via an active or directed mechanism as well as by diffusion. The limit of rapid interphase exchange leads to several distinct cases depending on the rate of reaction in the organelles and the storage capacity of the organelles. For a certain class of systems, marginally stable states are always oscillatory and small amplitude chemical waves can be propagated. Analysis of a one-component system shows that several distinct types of finite-amplitude waves can propagate unattenuated, each at a characteristic velocity. Thus a very simple reaction-transport system can lead to a very flexible chemical transmission line.