  Topological classification in our previous paper [K. Shiozaki and M. Sato,
Phys. Rev. B ${\bf 90}$, 165114 (2014)] is extended to nonsymmorphic
crystalline insulators and superconductors. Using the twisted equivariant
$K$-theory, we complete the classification of topological crystalline
insulators and superconductors in the presence of additional order-two
nonsymmorphic space group symmetries. The order-two nonsymmorphic space groups
include half lattice translation with $Z_2$ flip, glide, two-fold screw, and
their magnetic space groups. We find that the topological periodic table shows
modulo-2 periodicity in the number of flipped coordinates under the order-two
nonsymmorphic space group. It is pointed out that the nonsymmorphic space
groups allow $\mathbb{Z}_2$ topological phases even in the absence of
time-reversal and/or particle-hole symmetries. Furthermore, the coexistence of
the nonsymmorphic space group with the time-reversal and/or particle-hole
symmetries provides novel $\mathbb{Z}_4$ topological phases, which have not
been realized in ordinary topological insulators and superconductors. We
present model Hamiltonians of these new topological phases and the analytic
expression of the $\mathbb{Z}_2$ and $\mathbb{Z}_4$ topological invariants. The
half lattice translation with $Z_2$ spin flip and glide symmetry are compatible
with the existence of the boundary, leading to topological surface gapless
modes protected by such order-two nonsymmorphic symmetries. We also discuss
unique features of these gapless surface modes.
