  In this paper, the regularity properties of Cauchy problem for linear and
nonlinear nonlocal wave equations are studied.The equation involves a
convolution integral operators with a general kernel operator functions whose
Fourier transform are operator functions defined in Hilbert space H together
with some growth conditions. We establish local and global existence and
uniqueness of solutions assuming enough smoothness on the initial data and the
operator functions. By selecting the space H and the operators, the wide class
of wave equations in the field of physics are obtained.
