  We study two-dimensional noncentrosymmetric nodal superconductors under
Zeeman field and clarify the field angle dependence of topological properties.
It has been shown that the nodal excitation acquires an excitation gap due to
the Zeeman field perpendicular to anti-symmetric spin-orbit coupling, and then
gapful topological superconductivity is realized. We show that the system
undergoes gapful-gapless transition against tilting of the field. The gapless
phase remains to show a finite band gap and unusual Majorana edge states in
between the bulk bands. The Majorana edge states naturally propagate in a same
direction between oppositely-oriented edges. We elucidate relations of such
unidirectional Majorana edge states with chiral edge states in the gapful
topological superconducting phase and previously studied Majorana flat bands at
zero Zeeman field. A compact formula of topological invariants characterizing
the edge states is given. The gapful-gapless topological phase transition and
associated evolution of Majorana states are demonstrated in a model for
$D+p$-wave superconductivity. Experimental realization in recently fabricated
cuprate heterostructures and heavy fermion thin films is discussed.
