A stability characteristic of the Doi-Edwards viscoelastic constitutive equation is studied. Hadamard-type stability determined by the elastic part of the constitutive equation is considered in the case of simple flows. Criteria for general 3-D stability are derived in a complete biquadratic form, and rather simple algebraic condition under 1-D and 2-D disturbances is then formulated. Application of constraints to this rheological equation of state proves inevitable occurrence of the Hadamard-type instability in simple shear and uniaxial (or equi-biaxial) extensional flows, and the threshold of instability is calculated in terms of strain for all the flow types. The obtained values of critical strains are relatively low, hence it is thought that they can be easily achieved even in experiments as well as in industrial processing. We conclude that this instability is not at all related to real physical phenomena and it is merely inappropriateness owned by the constitutive equation.