  This paper is devoted to the construction of exponential integrators of first
and second order for the time discretization of constrained parabolic systems.
For this extend, we combine well-known exponential integrators for
unconstrained systems with the solution of certain saddle point problems in
order to meet the constraints throughout the integration process. The result is
a novel class of semi-explicit time integration schemes. We prove the expected
convergence rates and illustrate the performance on two numerical examples
including a parabolic equation with nonlinear dynamic boundary conditions.
