  Usually, in supersymmetric theories, it is assumed that the time-evolution of
states is determined by the Hamiltonian, through the Schr\"odinger equation.
Here we explore the superevolution of states in superspace, in which the
supercharges are the principal operators. The superevolution equation is
consistent with the Schr\"odinger equation, but it avoids the usual degeneracy
between bosonic and fermionic states. We discuss superevolution in
supersymmetric quantum mechanics and in a simple supersymmetric field theory.
