  We consider a variant of the Hegselmann-Krause model of consensus formation
where information between agents propagates with a finite speed $\mathfrak{c}$.
This leads to a system of ordinary differential equations (ODE) with
state-dependent delay. Observing that the classical well-posedness theory for
ODE systems does not apply, we provide a proof of global existence and
uniqueness of solutions of the model. We prove that asymptotic consensus is
always reached in the spatially one-dimensional setting of the model, as long
as agents travel slower than $\mathfrak{c}$. We also provide sufficient
conditions for asymptotic consensus in the spatially multi-dimensional setting.
