  Let ${\mathcal W}_n$ denote any of the three families of classical Weyl
groups: the symmetric groups ${\mathcal S}_n$, the hyperoctahedral groups
(signed permutation groups) ${\mathcal S}^B_n$, or the even-signed permutation
groups ${\mathcal S}^D_n$. In this paper we give an uniform construction of a
Hamilton cycle for the restriction to involutions on these three families of
groups with respect to a inverse-closed connecting set of involutions. This
Hamilton cycle is optimal with respect to the Hamming distance only for the
symmetric group ${\mathcal S}_n$.
  We also recall an optimal algorithm for a Gray code for type $B$ involutions.
A modification of this algorithm would provide a Gray Code for type $D$
involutions with Hamming distance two, which would be optimal. We give such a
construction for ${\mathcal S}^D_4$ and ${\mathcal S}^D_5$.
