Conventional simulation techniques to model the dynamics of proteins in atomic detail are restricted to short time scales. A simplified molecular description, in which high frequency motions with small amplitudes are ignored, can overcome this problem. In this protein model only the backbone dihedrals phi and psi and the chi(i) of the side chains serve as degrees of freedom. Bond angles and lengths are fixed at ideal geometry values provided by the standard molecular dynamics (MD) energy function CHARMM. In this work a Monte Carlo (MC) algorithm is used, whose elementary moves employ cooperative rotations in a small window of consecutive amide planes, leaving the polypeptide conformation outside of this window invariant. A single of these window MC moves generates local conformational changes only. But, the application of many such moves at different parts of the polypeptide backbone leads to global conformational changes. To account for the lack of flexibility in the protein model employed, the energy function used to evaluate conformational energies is split into sequentially neighbored and sequentially distant contributions. The sequentially neighbored part is represented by an effective (phi,psi)-torsion potential. It is derived from MD simulations of a flexible model dipeptide using a conventional MD energy function. To avoid exaggeration of hydrogen bonding strengths, the electrostatic interactions involving hydrogen atoms are scaled down at short distances. With these adjustments of the energy function, the rigid polypeptide model exhibits the same equilibrium distributions as obtained by conventional MD simulation with a fully flexible molecular model. Also, the same temperature dependence of the stability and build-up of alpha helices of 18-alanine as found in MD simulations is observed using the adapted energy function for MC simulations. Analyses of transition frequencies demonstrate that also dynamical aspects of MD trajectories are faithfully reproduced. Finally, it is demonstrated that even for high temperature unfolded polypeptides the MC simulation is more efficient by a factor of 10 than conventional MD simulations.