This paper generalizes the work of J. L. B. Cooper on symmetric operators in a Hilbert space to Pontrjagin and Krein spaces. Existence (and uniqueness) of a solution for Schrödinger’s equation dψ(t)/dt = iAψ(t), ψ(0) = φ∈Π [ = Π+(+̇)π̄] for the bounded decomposable symmetric operator A (the self-adjoint operator A) is studied. Also, the existence of a solution for (1/i)∂ψ(t)/∂t = A*ψ(t), ψ(0) = φ∈Π, where A is a cross-bounded symmetric operator in Π, is discussed. Finally, existence and uniqueness of the equation (1/i)(∂ψ(t)/∂t) = Aψ(t), ψ(0) = φ∈Πk, where A is a self-adjoint operator in the Pontrjagin space Πk, is studied, and the fact that the maps φ→ψ(t) form a group of unitary operators on Πk is deduced.