In the beam pipe of the Main Damping Ring (MDR) of the Next Linear Collider (NLC), ionization of residual gasses and secondary emission give rise to an electron-cloud which stabilizes to equilibrium after few bunch trains. In this paper, we present recent computer simulation results for the main features of the electron cloud at the NLC and preliminary simulation results for the TESLA main damping rings, obtained with the code POSINST that has been developed at LBNL, and lately in collaboration with SLAC, over the past 7 years. Possible remedies to mitigate the effect are also discussed. We have recently included the possibility to simulate different magnetic field configurations in our code including solenoid, quadrupole, sextupole and wiggler.