  We study graded connected algebras over a field of characteristic zero and
give an explicit formula for the cyclic homology of a tensor algebra. By means
of a slightly new definition of David Anick's notion "strongly free" we are
able to prove that cyclic homology of an algebra of global dimension two is
zero in homological degree greater than one and is zero also in homological
degree equal to one in case the relations are monomials. We give also explicit
formulas for the cyclic homology of a tensor algebra modulo one symmetric
quadratic form.
