Let  be a positive integer such that c and  are square-free. We consider the infinite parametric family of bicyclic biquadratic fields  We determine the integral basis of the field. We show that K admits no power integral basis, determine the minimal index and all elements of minimal index. We use the solutions of a parametric family of quartic Thue equations and extensive numerical calculations by Maple and Magma.

bicyclic biquadratic fields, power integral basis, minimal index.