Summary: We consider a macroscopic quantum system with unitarily evolving pure state \(\psi_t\in \mathcal{H}\) and take it for granted that different macro states correspond to mutually orthogonal, high-dimensional subspaces \(\mathcal{H}_{\nu}\) (macro spaces) of \(\mathcal{H}\). Let \(P_{\nu}\) denote the projection to \(\mathcal{H}_{\nu}\). We prove two facts about the evolution of the superposition weights \(\Vert P_{\nu} \psi_t\Vert^2\): First, given any \(T>0\), for most initial states \(\psi_0\) from any particular macro space \(\mathcal{H}_{\mu}\) (possibly far from thermal equilibrium), the curve \(t\mapsto \Vert P_{\nu} \psi_t\Vert^2\) is approximately the same (i.e., nearly independent of \(\psi_0)\) on the time interval \([0, T]\). And second, for most \(\psi_0\) from \(\mathcal{H}_{\mu}\) and most \(t\in [0,\infty), \Vert P_{\nu} \psi_t\Vert^2\) is close to a value \(M_{\mu\nu}\) that is independent of both \(t\) and \(\psi_0\). The first is an instance of the phenomenon of dynamical typicality observed by Bartsch, Gemmer, and Reimann, and the second modifies, extends, and in a way simplifies the concept, introduced by von Neumann, now known as normal typicality.