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Coset conformal field theories with abelian isotropy groups. Abstract Conformal field theories based on g/u(1) d coset constructions where g is a reductive algebra are studied.It is shown that the theories are equivalent to constrained WZNW models for g. Generators of extended symmetry algebras and primary fields are constructed. In a recent paper [1] currents, primary fields and generators of disctete symmetry groups of g/u(1) d , d = 1,. .. rank g, coset conformal field theories [2, 3] for simple Lie algebras g were constructed.The construction is based on operator quantization of the WZNW theory for g with the constrained affine Lie algebrâ u(1) d associated with u(1) d. In this article we consider the g/u(1) d coset theory where g is a direct sum of simple and abelian Lie algebras.Using a version of the generalized canonical quantization method [4, 1] we show that this theory is equivalent to a constrained WZNW theory and find parafermionic currents and primary fields.They are expressed in terms of the initial fields and free bosons.The theory has a discrete symmetry group which is generated by an abelian subalgebra of g. Studies of such theories were initiated in [5] where su(2)/u(1) parafermionic algebra was constructed and it was shown that the corresponding theory describes a critical system.