Max-min algebra is an algebraic structure in which classical addition and multiplication are replaced by ⊕ and \kr, where a⊕b=max{a,b},a\krb=min{a,b}. The notation \mbfA\kr\mbfx=\mbfb represents an interval system of linear equations, where \mbfA=[\pA,\nA], \mbfb=[\pb,\nb] are given interval matrix and interval vector, respectively, and a solution is from a given interval vector \mbfx=[\px,\nx]. We define six types of solvability of max-min interval systems with bounded solution and give necessary and sufficient conditions for them.