  A stability criterion is derived in general relativity for self-similar
solutions with a scalar field and those with a stiff fluid, which is a perfect
fluid with the equation of state $P=\rho$. A wide class of self-similar
solutions turn out to be unstable against kink mode perturbation. According to
the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be
a critical solution for the spherical collapse of a stiff fluid if we allow
sufficiently small discontinuity in the density gradient field in the initial
data sets. The self-similar scalar-field solution, which was recently found
numerically by Brady {\it et al.} (2002 {\it Class. Quantum. Grav.} {\bf 19}
6359), is also unstable. Both the flat Friedmann universe with a scalar field
and that with a stiff fluid suffer from kink instability at the particle
horizon scale.
