The stability of a steady, axisymmetric, laminar, primary flow composed of two fluids flowing concentrically in a straight circular tube is investigated by the method of small perturbations. Both asymmetric and axisymmetric disturbances to the primary flow are considered. It is demonstrated that, regardless of the size of the Reynolds number, no situations are encountered for which the primary flow is stable to both types of disturbances, simultaneously. The primary cause of instability is found to be the difference in viscosities of the two fluids.