This research project studies the stochastic processes of Taiwan's stock returns. Lee's (1989) unified approach to examine the stochastic behavior of Taiwan's stock returns is adopted. A nested likelihood ratio tests are also performed to identify a better stochastic description of Taiwan's stock returns. After studying 195 stocks' monthly returns from January 1972 to June 1994, I find results similar to Lee's finding with the U.S. data. A pure random walk with a drift model is soundly rejected. A complicated Oldfield et al. (1977) model is not only difficult to estimate but also not giving a better result compared to simpler alternative models. Unlike Lee's negative autocorrelation result, however, the correlation between jumps are highly positive, in any, for Taiwan's stock returns. The nested likelihood ratio tests indicate that a random walk with a non zero drift in combination with a non zero jump is a better model in describing Taiwan's stock return behavior. This is true for both the Poisson-type and Bernoulli-type jump. All the previous studies by Press (1967), Beckers (1981), and Ball and Torous (1983) are worse than the corresponding more complete model. The size and volatility of the jump is clearly higher than those of the random walk. It seems that Taiwan's stock market reacts to economic information sharply, and overtime, such reaction is positive in average. Without inflow of substantial information, which is unlikely in a month time span, Taiwan's stock returns would follow a random walk with a minimal drift in average.