In this note, we extend our recent work for the heat equation in [1] and compare numerically continuous Galerkin-Petrov (cGP) and discontinuous Galerkin (dG) time discretizations for the nonstationary Stokes equations in two dimensions. For the space discretization, we
use the LBB-stable finite element pair Q2=Pdisc 1 and we discuss implementation aspects as well as methods for solving the resulting block systems which are treated by using monolithic multigrid solvers with Vanka-type smoothers. By means of numerical experiments we compare the dierent time discretizations w.r.t. accuracy and computational costs and we show that the convergence behavior of the multigrid method is almost independent of mesh size and time step leading to an efficient solution process.