BR0-distributivity has an important position in the structure of BR0algebras which says a→b∨c=(a→b)∨(a→c). It is proved that residuated lattices with BR0-distributivity also have good properties. BR0-distributivity is introduced in residuated lattices, and its equivalent form is given. Then the BR0-distributivity is generalized in complete residuated lattices, and BR0-first infinite distributivity and BR0-second infinite distributivity are obtained. Finally, the properties and relationship between two kinds of BR0-infinite distributivity are discussed in regular complete residuated lattices and the unite interval ［0,1］, respectively.