  The P\'{o}lya group of an algebraic number field is the subgroup generated by
the ideal classes of the products of prime ideals of equal norm inside the
ideal class group. Inspired by a recent work on consecutive quadratic fields
with large class numbers by Cherubini et al., we extend the notion of {\it
consecutiveness} of number fields to certain parametric families of cyclic
cubic fields and bi-quadratic fields and address the question of the existence
of infinitely many such consecutive fields with large P\'{o}lya groups. This
extends a recent result of the second author and Saikia for totally real
bi-quadratic fields.
