The security of double block length hash functions and their compression functions is analyzed in this paper. First, the analysis of double block length hash functions by Satoh, Haga, and Kurosawa is investigated. The focus of this investigation is their analysis of the double block length hash functions with the rate 1 whose compression functions consist of a block cipher with the key twice longer than the plaintext/ciphertext. It is shown that there exists a case uncovered by their analysis. Second, the compression functions are analyzed with which secure double block length hash functions may be constructed. The analysis shows that these compression functions are at most as secure as the compression functions of single block length hash functions.