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SNR model computation results have been obtained which indicate that the radial distribution of soft X-ray and forbidden coronal Fe surface brightnesses in adiabatic, middle-aged SNRs can be used as a basis of discrimination for whether the equilibration time is short or long, by comparison with the ionization time-scale. These models are based on a grid of Sedov-Taylor models with time-dependent, nonequilibrium collisional ionization of 13 chemical elements; the two extreme equilibration conditions assumed are T(ion) = T(e) and a Coulomb equilibration of ion and electron temperatures. The models are compared with data taken from X-ray images of the Cygnus Loop and Puppis A.