The time-dependent Stokes problem is solved using continuous, piecewise linear finite elements and a classical stabilization procedure. Four order-one methods are proposed for the time discretization. The first one is nothing but the Euler backward scheme and requires a large linear system involving the velocity and pressure unknowns to be solved. The other three schemes allow velocity and pressure computations to be decoupled, namely the pressure-matrix method, a method based on an inexact LU factorization, and an operator splitting method. Stability and condition number estimates are derived. Numerical experiments in two space dimensions confirm the theoretical predictions. (C) 2001 John Wiley & Sons, Inc.