  Individual components of well-detached binary systems are assumed to be two
single-like stars with a common origin, i.e. they share the same chemical
composition and same age. Therefore, one expects to fit the observed parameters
of both components with a single isochrone at the same metallicity. We show
that serious problems appear for systems with accurate fundamental data
(eclipsing binaries in the field and in the Hyades, and a visual binary) in the
0.7-1.1 Msun mass range. We discuss and briefly review the results obtained so
far on these objects. Finally, in an attempt to solve this problem, we present
new projects, both on the theoretical and the observational sides.
