By means of variational structure and Z 2 group index theory, we obtain multiple periodic solutions to a class of second-order mixed-type differential equations x ' ' ( t − τ ) + f ( t , x ( t ) , x ( t − τ ) , x ( t − 2 τ ) ) = 0 and x ' ' ( t − τ ) + λ ( t ) f 1 ( t , x ( t ) , x ( t − τ ) , x ( t − 2 τ ) ) = x ( t − τ ) .