The result (proved in Part I) that
Diff
(
D
n
,
∂
)
≃
Ω
n
+
1
(
PL
n
/
O
n
)
{\operatorname {Diff}}({D^n},\partial ) \simeq {\Omega ^{n + 1}}({\text {PL}_n}/{O_n})
is used to compute some new homotopy of
Diff
(
D
n
,
∂
D
n
)
{\operatorname {Diff}}({D^n},\partial {D^n})
. The relation between smooth and PL pseudo-isotopy is explored. Known and new results on the homotopy of
PL
n
{\text {PL}_n}
are summarized.