Distinguished involutions in the affine Weyl groups, defined
by G. Lusztig, play an essential role in the Kazhdan-Lusztig combinatorics of
these groups. A distinguished involution is called canonical if it is the
shortest element in its double coset with respect to the finite Weyl group.
Each two-sided cell in the affine Weyl group contains precisely one canonical
distinguished involution. We calculate the canonical
distinguished involutions in the affine Weyl groups of rank ≤ 7. We also
prove some partial results relating canonical distinguished involutions and
Dynkin's diagrams of the nilpotent orbits in the Langlands dual group.