Pulsed neutron experiments in very large homogeneous systems are useful in estimating fundamental-mode decay constants even though it is impossible for an asymptotic mode ever to be completely established. Experimental results in water show that the observed decay of the neutron density is very nearly exponential and that the decay constant is close to the asymptotic value. A comparison of some relatively simple theoretical models illustrates the significance of fast neutron dispersion and the very poor prediction obtained, even qualitatively, using one-group time-dependent diffusion theory.