Ladies pass back R to R, give R hands to partners, and turn underarm into ceili hold.
Step dance and Ceili are also directly descended from the Celtic tradition.
Less competitive and more social are the Ceili dances, which are based on a dance form from France called the quadrille (which also happens to be the ancestor of the square dance in America).
In fact, the term "ceili" also represents a party-like gathering of musicians and dancers, often gathering at a pub to share the traditional sounds and steps together.