The authors study convergence of implicit monotone schemes for multiphase flow in porous media. In particular to stabilise the approximation the so-called phase-based upwinding is used. It is shown that the nonlinear Gauss-Seidel or Jacobi algorithms converge for a scheme with implicit time-stepping. In particular they obtained an alternative proof that for one-dimensional problems the scheme converges to the entropy solution of the conservation laws for arbitrary CFL numbers. At the end of paper the accuracy of phase-based upstream scheme is studied.