Feller property of some diffusion processes and the time changed
processes is investigated. Diffusion processes treated here
are skew product of one dimensional generalized diffusion
processes and the spherical Brownian motion, and the time
changed processes are given by additive functional associated
with some underlying measure. Concrete expressions of the
Dirichlet forms corresponding to time changed processes are
also obtained, which may be of non-local type caused by degeneracy
of the underlying measures.