  We investigate the dynamical relaxation behavior of the two-point correlation
in extended XY models with a gapless phase after quenches from various initial
states. Specifically, we study the XY chain with gapless phase induced by the
additional interactions: Dzyaloshinskii-Moriya interaction and XZY-YZX type of
three-site interaction. When quenching from the gapped phase, we observe that
the additional interactions have no effect on the relaxation behavior. The
relaxation behavior is $\delta C_{mn}(t)\sim t^{-3/2}$ and $\sim t^{-1/2}$ for
the quench to the commensurate phase and the incommensurate phase,
respectively. However, when quenching from the gapless phase, we demonstrate
that the scaling behavior of $\delta C_{mn}(t)$ is changed to $\sim t^{-1}$ for
the quench to the commensurate phase, and the decay of $\delta C_{mn}(t)$
follows $\sim t^{-1}$ or $\sim t^{-1/2}$ for the quench to the incommensurate
phase depending on the parameters of pre-quench Hamiltonian. We also establish
the dynamical phase diagrams based on the dynamical relaxation behavior of
$\delta C_{mn}(t)$ in the extended XY models.
