Overnight Federal funds and overnight Eurodollars are among the most liquid short-term assets that a bank can hold to acquire required reserves. They are traded overnight and denominated in U.S. dollars. They also have different characteristics: The Fed funds market and the Eurodollar market are located in different places, and the transaction volume is larger in the overnight Eurodollar market than in the Fed funds market. This paper is an empirical work on the relationship between the Federal funds rate and the overnight Eurodollar rate. Hamilton (1996) found that the Fed funds rate exhibited calendar day effects over 1984-1990. I find that the overnight Eurodollar rate exhibits very similar calendar day effects but the absolute magnitudes are slightly less in general over 1984-1997. The empirical results support the hypothesis that the tendency in daily changes in the Federal funds rate and in the overnight Eurodollar rate are caused by line limits, transaction costs and accounting convention in the Federal funds market. The differential between the Fed funds rate and the overnight Eurodollar rate is predictable and it possibly provides the evidence against the efficient market hypothesis.