Let G be a Chevalley group over a field K. Every subgroup of G which is conjugate in G with a subgroup \(X_{\alpha}=\{x_{\alpha}(t)|\) \(t\in K\}\) for a long root \(\alpha\) is called a long root subgroup. The author shows that for any two long root subgroups \(X_ 1\) and \(X_ 2\) one of the following possibilities occurs. (1) \(X_ 1\), \(X_ 2\) commute and \(<X_ 1,X_ 2>\) contains (i) a long root subgroup different from \(X_ 1\), \(X_ 2\); (ii) no long root subgroup different from \(X_ 1\), \(X_ 2\). (2) \(<X_ 1,X_ 2>\) is a group isomorphic to the group of \(3\times 3\) upper unitriangular matrices. (3) \(<X_ 1,X_ 2>\) is isomorphic to SL(2,K) or PSL(2,K).