  E. Thomas was one of the first to solve an infinite family of Thue equations,
when he considered the forms $F_n(X, Y )= X^3 -(n-1)X^2Y -(n+2)XY^2 -Y^3$ and
the family of equations $F_n(X, Y )=\pm 1$, $n\in {\mathbf N}$. This family is
associated to the family of the simplest cubic fields ${\mathbf Q}(\lambda)$ of
D. Shanks, $\lambda$ being a root of $F_n(X,1)$. We introduce in this family a
second parameter by replacing the roots of the minimal polynomial $F_n(X, 1) $
of $\lambda$ by the $a$-th powers of the roots and we effectively solve the
family of Thue equations that we obtain and which depends now on the two
parameters $n$ and $a$.
