  In additional to the parity ($\mathcal{P}$) symmetric, time reversal
($\mathcal{T}$) symmetric, and $\mathcal{PT}$ symmetric nonlocal integrable
systems, some other types of nonlocal integrable Klein-Gordon models with the
space-time exchange nonlocality and the moving nolocality are proposed. The Lax
pairs of the established nonlinear nonlocal Klein-Gordon equations are
explicitly given. A special soliton solution, composed of
$\mathcal{PT}$-symmetric part and $\mathcal{PT}$-antisymmetric part, is
illustrated with the shape change.
