  We introduce a procedure to identify very soft X-ray sources (VSSs) in
external galaxies. Our immediate goal was to formulate a systematic procedure
to identify luminous supersoft X-ray sources (SSSs), so as to allow comparisons
among galaxies and to study environmental effects. The focus of this paper is
on the design of the selection algorithm and on its application to simulated
data. In the companion paper we test it by applying it to sources discovered
through Chandra observations of 4 galaxies. We find that, in its application to
both simulated and real data, our procedure also selects somewhat harder
sources, which we call quasisoft. Whereas values of kT for SSSs are typically
tens of eV, some quasisoft sources (QSSs) may have kT as high as ~250-300 eV.
The dominant spectral component of other QSSs may be as soft as SSS spectra,
but the spectra may also include a low-luminosity harder component. We sketch
physical models for both supersoft and quasisoft sources. Some SSSs are likely
to be accreting white dwarfs; some of these may be progenitors of Type Ia
supernovae. Most QSSs may be too hot to be white dwarfs. They, together with a
subset of SSSs, may be neutron stars or, perhaps most likely, accreting
intermediate-mass black holes.
