  Two-place nonlocal systems have attracted many scientists' attentions. In
this paper, two-place non-localities are extended to multi-place
non-localities. Especially, various two-place and four-place nonlocal nonlinear
Schrodinger (NLS) systems and Kadomtsev-Petviashvili (KP) equations are
systematically obtained from the discrete symmetry reductions of the coupled
local systems. The Lax pairs for the two-place and four-place nonlocal NLS and
KP equations are explicitly given. Some types of exact solutions especially the
multiple soliton solutions for two-place and four-place KP equations are
investigated by means of the group symmetric-antisymmetric separation approach.
