The　bond　curvature　(K),　derived　from　the　Directional-Curvature　Theory,　is　developed　as　a　simple　and　efficient　criterion　for　structures　and　chemical　anisotropy　of　sidewall　[2+1]　cycloadditions　on　single-walled　boron　nitride　nanotubes　(SWBNNTs).　The　origin　of　the　relationship　between　the　chemical　anisotropy　of　SWBNNTs　and　the　bond　curvature　is　explained　based　on　the　viewpoint　of　hybrid　orbital　theory.　The　first-principle　calculations　for　the　additions　on　various　types　of　the　SWBNNTs　show　that　not　those　single-parameter　criteria,　but　the　K,　in　which　the　two　parameters　R　and　θ　are　involved,　can　solely　determine　the　structure　types　of　the　cycloadditions　on　the　B-N　bonds　and　predict　the　chemical　anisotropy　of　the　SWBNNTs.　The　larger　the　K　is,　the　more　easily　the　B-N　bond　is　broken,　and　the　binding　energies　of　the　opened　structures　change　linearly　with　K.　For　the　cycloaddition　on　SWBNNTs　with　moderate　diameter,　the　boundary　of　K　for　determining　whether　the　B-N　bond　is　broken　or　not　is　about　1.45　nm　-1　.　©　2008　American　Chemical　Society.