Reversible algorithms for Nod-Hoover chain (NHC) dynamics are developed by simple extensions of Verlet-type algorithms: leap frog, position Verlet, and velocity Verlet. Tests for a model one dimensional harmonic oscillator show that they generate proper canonical distributions and are stable even with a large time step. Using these algorithms, the effects of the Nose mass and chain length are examined. For a chain length of two, the sampling efficiency is much more sensitive to the Nose mass than for a longer chain of length four. This indicates that the chain length in general should be longer than two. The noniterative nature of the algorithms allows them to be easily adapted for constraint dynamics. For the most general case where multiple NHC's are coupled to a system with constraints, a correction of the first Nose acceleration is required, which is derived from the continuity equation on a constrained hypersurface of the phase space. Tests for model systems of two and three coupled harmonic oscillators with one normal mode constrained show that these algorithms, in combination with the corrected dynamical equations, sample the canonical distributions for the unconstrained degrees of freedom. (C) 1997 American Institute of Physics.