  We propose and study a nonlocal Euler system with relaxation, which tends to
a strictly hyperbolic system under the hyperbolic scaling limit. An independent
proof of the local existence and uniqueness of this system is presented in any
spatial dimension. We further derive a precise critical threshold for this
system in one dimensional setting. Our result reveals that such nonlocal system
admits global smooth solutions for a large class of initial data. Thus, the
nonlocal velocity regularizes the generic finite-time breakdown in the
pressureless Euler system.
