  The geometric phases of a two-level atom interacting with non-Markovian
environments are calculated and the non-Markovian effects on the geometric
phases are discussed in this paper. Three kinds of methods that describe the
non-Markovian process, projection superoperator technique, memory kernel master
equation and post-Markovian master equation, are used in the discussions. The
results show that when the dissipation rate is large, the non-Markovian effects
change the geometric phase more strikingly than the small one.
