  Many main-sequence F and early G stars are too luminous for their effective
temperature, surface gravity, and chemical composition. These {\it overluminous
stars} have two curious properties. First, their kinematics as a function of
age from stellar evolution modeling (isochrone fitting) is very different from
that of normal stars. Second, while X-ray luminosity of normal stars declines
with age, the X-ray luminosity of overluminous F stars changes in the opposite
direction, being on average higher for older stars. These properties imply
that, in defiance of standard models of stellar evolution, F stars of a given
mass and chemical composition can evolve very differently. Assuming that the
models correctly describe normal stars, for overluminous F stars they predict
too young age and the X-ray emission evolving in the direction opposite to the
actually observed trend. This discrepancy between modeling results and
observational data suggests that standard stellar evolution models and models
of stellar activity are missing some important factors, which makes stellar age
and predictions for stellar activity from these models problematic. The data
and literature analysis presented in this paper point to a nonuniform rotation
of the stellar interior as a plausible key factor able to reconcile the
divergent trends in age-velocity relationships of normal and overluminous F
stars and explain in a coherent and self-consistent way the overluminosity
phenomenon.
