The purpose of this paper is to examine whether firm size and book-to-market equity ratio have an explanatory power of the average returns of stocks listed on the Athens Stock Exchange (ASE) for the 1997-2000 period. The motivation for this research has been the previous empirical evidence about the non-existence of the CAPM's validity in the ASE as well as the influence of many articles about the association of stocks' expected returns with other factors, like firm capitalization, dividend yield, leverage, eamings-per-prjce and book-to-market equity. In spite of the fact that the Greek Stock Market is inefficient relative to other stock markets in various parts of the world, the results of the present paper were nearly similar to those found by other researchers using data drawn from other countries. We employed the simple ordinary least squares and showed that size and book-to-market equity along with the market factor do a good job explaining the average returns on ASE stocks for the period under investigation. Especially the size factor seems to exert a more significant influence on share returns compared to the book-to-market equity factor. We also applied stability tests, using the recursive coefficients estimation model, in order to trace the evolution of estimates for the regression coefficients and found evidence that the coefficients display an insignificant variance during the 1997-2000 period, which is an indication of stability. This paper contributes to the literature in the sense that it extends the international empirical evidence oil the aforementioned size and book-to-market effects on the average stock returns and also provides additional insight into the relative explanatory power of the existing theories.