  For an equifocal submanifold $M$ with non-flat section in an irreducible
simply connected symmetric space $G/K$ of compact type, it is known that the
sections of $M$ are spheres or real projective spaces. In this paper, we first
construct a topological Tits building (of spherical type) associated to $M$ in
the case where the sections of $M$ are spheres, and, by using the building, we
show that the codimension of $M$ equals to two when the sections of $M$ are
spheres. Also, we estimate the codimension of $M$ from above by using the
multiplicities of the roots of the root system of $G/K$, where we do not need
assume that the sections of $M$ are spheres. As its result, we can show that
there exists no equifocal submanifold with non-flat section in some irreducible
simply connected symmetric spaces of compact type.
