A recently proposed analytical hemodynamic model1 [S. Fantini, NeuroImage 85, 202–221 (2014)] is able to predict the changes of oxy, deoxy, and total hemoglobin concentrations (model outputs) given arbitrary changes in blood flow, blood volume, and rate of oxygen consumption (model inputs). One assumption of this model is that the capillary compartment is characterized by a single blood transit time. In this work, we have extended the original model by considering a distribution of capillary transit times and we have compared the outputs of both models (original and extended) for the case of sinusoidal input signals at different frequencies, which realizes the new technique of coherent hemodynamics spectroscopy (CHS). For the calculations with the original model, we have used the mean value of the distribution of capillary transit times considered in the extended model. We have found that, for distributions of capillary transit times having mean values around 1 s and a standard deviation less than about 45% of the mean value, the original and extended models yield the same CHS spectra (i.e., model outputs versus frequency of oscillation) within typical experimental errors. For wider capillary transit time distributions, the two models yield different CHS spectra. By assuming that Poiseuille's law is valid in the capillary compartment, we have related the distribution of capillary transit times to the distributions of capillary lengths and capillary speed of blood flow to calculate the average capillary and venous saturations. We have found that, for standard deviations of the capillary transit time distribution that are less than about 80% of the mean value, the average capillary saturation is always larger than the venous saturation. By contrast, the average capillary saturation may be less than the venous saturation for wider distributions of the capillary transit times.