  We present the results of a systematic study using ASCA of the ionization
state for six ``mixed-morphology'' supernova emnants (MMSNRs): IC 443, W49B,
W28, W44, 3C391, and Kes 27. MMSNRs show centrally filled thermal X-ray
emission, which contrasts to shell-like radio morphology, a set of
haracteristics at odds with the standard model of SNR evolution (e.g., the
Sedov model). We have therefore studied the evolution of the MMSNRs from the
ionization conditions inferred from the X-ray spectra, independent of X-ray
morphology. We find highly ionized plasmas approaching ionization equilibrium
in all the mmsnrs. The degree of ionization is systematically higher than the
plasma usually seen in shell-like SNRs. Radial temperature gradients are also
observed in five remnants, with cooler plasma toward the limb. In IC 443 and
W49B, we find a plasma structure consistent with shell-like SNRs, suggesting
that at least some MMSNRs have experienced similar evolution to shell-like
SNRs. In addition to the results above, we have discovered an ``overionized''
ionization state in W49B, in addition to that previously found in IC 443.
Thermal conduction can cause the hot interior plasma to become overionized by
reducing the temperature and density gradients, leading to an interior density
increase and temperature decrease. Therefore, we suggest that the
``center-filled'' X-ray morphology develops as the result of thermal
conduction, and should arise in all SNRs. This is consistent with the results
that MMSNRs are near collisional ionization equilibrium since the conduction
timescale is roughly similar to the ionization timescale. Hence, we conclude
that MMSNRs are those that have evolved over$\sim10^4$ yr. We call this phase
as the ``conduction phase.''
