  Based on the first-principles calculations and experimental measurements, we
report that the hexagonal phase of ternary transition metal pnictides TT'X
(T=Zr, Hf; T'=Ru; X=P, As), which are well-known noncentrosymmetric
superconductors with relatively high transition temperatures, host nontrivial
bulk topology. Before the superconducting phase transition, we find that HfRuP
belongs to a Weyl semimetal phase with 12 pairs of type-II Weyl points, while
ZrRuAs, ZrRuP and HfRuAs belong to a topological crystalline insulating phase
with trivial Fu-Kane $\mathbb Z_2$ indices but $nontrivial$ mirror Chern
numbers. High-quality single crystal samples of the noncentrosymmetric
superconductors with these two different topological states have been obtained
and the superconductivity is verified experimentally. The wide-range band
structures of ZrRuAs have been identified by ARPES and reproduced by
theoretical calculations. Combined with intrinsic superconductivity, the
nontrivial topology of the normal state may generate unconventional
superconductivity in both bulk and surfaces. Our findings could largely inspire
the experimental searching for possible topological superconductivity in these
compounds.
