  Cosmological dynamics of scalar field with a monomial potential $\phi^{n}$
with a general background equation of state is revisited. It is known that if
$n$ is smaller than a critical value, the scalar field exhibits a coherent
oscillation and if $n$ is larger it obeys a scaling solution without
oscillation. We study in detail the case where $n$ is equal to the critical
value, and find a peculiar scalar dynamics which is neither oscillating nor
scaling solution, and we call it a pseudo scaling solution. We also discuss
cosmological implications of a pseudo scaling scalar dynamics, such as the
curvature perturbation and the domain wall problem.
