  We study the equivariant concordance classes of two-bridge knots, providing
an easy formula to compute their butterfly polynomial, and we give two
different proofs that no two-bridge knot is equivariantly slice. Finally, we
introduce a new invariant of equivariant concordance for strongly invertible
knots. Using this invariant as an obstruction we strengthen the result on
two-bridge knots, proving that their equivariant concordance order is always
infinite.
