Measurements of the mutual diffusion coefficients (D) of the liganded human hemoglobins (Hb) oxy-HbA and oxy-HbS were performed as a function of Hb concentration (CHb), pH, and ionic strength (tau) by intensity fluctuation spectroscopy (IFS). Average diffusion coefficients, (D), and normalized variances, ((D/(D) - 1)2), were recorded. Results are reported and select features are discussed quantitatively. (a) for tau = 0.15 M, the shape of the (d) vs. CHb curve is found to vary with pH. We developed a precise description of this effect in the form of an algebraic relationship between (D), CHb, and Z, the titration charge. (b) only slight differences between the (D) values of oxy-HbS and oxy-HbA are observed, at tau = 0.15 M, for CHb Less Than or Equal To 10 g%. These differences are explained by the theory of part a. (c) No evidence of aggregation is found in solutions of oxy-HbA or oxy-HbS, at tau = 0.15 M, for CHb Less Than or Equal To 10 g%. (d) Indications of aggregation appear in oxy-HbA solutions at very low concentrations of salt. An estimate is made of the extent of aggregation, and the average radius of a cluster is determined.