  Spectral singularities such as exceptional points invoke specific physical
effects. The present paper focuses upon the time dependent solutions of the
Schr\"odinger equation. In a simple model it is demonstrated that - depending
on initial conditions - within close proximity of exceptional points the time
behaviour of the wave function displays characteristic features such as very
fast decay or the opposite, i.e. very long life time. At the exceptional point
the wave function typically has a linear term in time besides the usual
exponential behaviour.
