By observing the lateral cephalometric radiograms of the Naso-pharynx of the mouth breatheres with adenoid hyperplasia, orthodontists could use the discriminant function as the supplementary diagnotic aid for the malocclusion cases with mouth breating. The purpose of this study was to ustilize the discriminant function as the indicator to remove the etiologic factor producing the relapse. The author used the 19 boys and 20 girls, who were the nasal-breathers with normal occlusion as the control group, and 16 boys 20 girls, who were the mouth breathers with adenoid hypaplasia and malocclusion. The age of the both groups was ranged from 12ys to 15ys. Results were as following ; 1. There was the difference in the bony structure of Naso-Pharynx between the mouth-breathers nasal-breathers. 2. IMRA of the mouth breathers was smaller than the nasal breathers. 3. The mouth-breathers had the skeletal open bite tendency. 4. Discriminant function; D_i-9.85374 + ax₂ +bx₄ +cx₆ + dx₇ + ex₈ a=-0.1211273 b=-0.5908992 c==1.508446 d=-1.541869 e=-1.404478