  We argue the emergence of nodal excitations due to the coupling with static
antiferromagnetic order in fully-gapped superconducting states in both cases
with and without inversion symmetry. This line node structure is not
accompanied with the sign change of the superconducting gap, in contrast to
usual unconventional Cooper pairs with higher angular momenta. In the case
without inversion symmetry, the stability of the nodal excitations crucially
depends on the direction of the antiferromagnetic staggered magnetic moment. A
possible realization of this phenomenon in CePt$_3$Si is discussed.
