  We propose a new method for Hybrid Monte Carlo (HMC) simulations with odd
numbers of dynamical fermions on the lattice. It employs a different approach
from polynomial or rational HMC. In this method, gamma-five hermiticity of the
lattice Dirac operators is crucial and it can be applied to Wilson,
domain-wall, and overlap fermions. We compare HMC simulations with two
degenerate flavors and (1 + 1) degenerate flavors using optimal domain-wall
fermions. The ratio of the efficiency, (number of accepted trajectories) /
(simulation time), is about 3:2. The relation between pseudofermion action of
chirally symmetric lattice fermions in four-dimensional(overlap) and
five-dimensional(domain-wall) representation are also analyzed.
