We investigate the sufficient conditions
and the necessary conditions on an exchange ring R under
which R has stable range one. These give nontrivial
generalizations of Theorem 3 of V. P. Camillo and H.-P. Yu (1995),
Theorem 4.19 of K. R. Goodearl (1979, 1991),
Theorem 2 of R. E. Hartwig (1982), and Theorem 9 of H.-P. Yu (1995).