Water solutions of ethyl(hydroxyethyl)cellulose have been investigated with the PFG NMR technique and by means of H-1 NMR relaxation measurements. The echo decays in PFG experiments have been recorded for EHEC with concentrations ranging from the dilute (c < c*) to the semidilute (c > c*). In addition, the temperature dependence of the echo decay was investigated. It is shown that the echo decays deviate substantially from Gaussian diffusion behavior. We discuss this in terms of polydispersity, aggregation, and scaling effects. It is argued that the observed deviations are too large to be caused by polydispersity effects alone. We base this conclusion on the observation that the molar mass scaling of the polymer diffusion coefficient goes roughly as M-4. We focus on using a log-normal distribution of diffusion coefficients in the evaluation procedure of the PFG data. It is found that by comparing the diffusion coefficients extracted from this type of procedure with "D-mean" as extracted from a "stretched exponential" approach, there is a difference in the evaluated diffusion constant by up to 1 order of magnitude. The difference depends on the degree of deviation from linear behavior in the echo decay when represented in a logarithmic plot vs the relevant experimental parameter.