New scaling regimes exist, for large distances and sufficiently long-ranged initial conditions, in the kinetics of directed spin models. The spatial length scales are larger than those found in spatially isotropic dynamic scaling. Their dynamical symmetries are given by the meta-conformal and the meta-Schrödinger algebras. These facts are illustrated through the exact solution of the directed spherical model at \(T\le T_c\) and compared with the 1D directed Glauber-Ising model at \(T=0\) .