In canonMuch like Tomo and Yomi (who are also paired), Yukari and Nyamo are long-time friends who keep each other company even though they are totally different in personality. Yukari, whose student equivalent is Tomo, is more immature and childish than her best friend Minamo (who resembles Yomi) though she also possesses these characteristics to a certain degree.
Yukari and Nyamo went to high school together, and now that they are grown up, they are both teachers at that same school. Neither one of them is married or has a romantic relationship throughout the series – Yukari even still lives with her mother. Nyamo usually visits Yukari's house every once in a while, and drives her to work. She is annoyed at Yukari because the only times Yukari visits her instead, is so that she can sleep there. In their spare time, they often go out for drinks, watch movies, and play video games.
Once, they went to see the movie Runaway Bride together, and when Yukari told her class about this, she lied and said that she had been on a date.
Some details about the two friends' past are clouded. For example, Yukari claims that Nyamo was recently in a relationship, but it is never revealed with whom. Yukari also blackmailed Nyamo once when she was about to tell Chihiro about what Yukari was like as a teenager by threatening to reveal information on a mysterious "love letter" of Nyamo's.Sometimes they discuss single life – an example is during vacations spent at Chiyo's summer house when their students wanted to find out details on their sex lives. Yukari's was not particularly interesting since she only replied by saying that there was nothing wrong with being single, and Nyamo told the girls particularly dirty stories when she drank a lot of alcohol only to prevent Yukari from doing it instead. In the manga, it is also speculated that Yukari may scare off men by just being herself. Nyamo seems particularly focused on getting married. At one point she visited a shrine at New Year's that was supposed to bring good luck for future marriages.
Aside from being friends, they are also rivals and get annoyed at each other. One area where they compete endlessly is teaching – who is more well-liked by her class and gets the nicest birthday gifts and who teaches the hardest subject (Yukari frequently accuses Nyamo of being dumb because she is a P.E. teacher while Yukari is an English teacher). Yukari is also very focused on winning every sports festival, because of a tradition of making bets with Nyamo on the outcomes (if one of them wins the other has to pay for a yakiniku feast). Yukari even transferred the athlete Kagura to her class because she thought it would give her class a better chance of winning upcoming sports festivals.
NYukari is one of the most popular Azumanga Daioh pairings, since the two teachers are sometimes seen as more or less life partners, always spending time together even after high school graduation. Their ever-present love-hate relationship also contributes, and probably the fact that they are both single grown-ups. Some fans have even interpreted the love letter event as concerning a letter sent to Yukari from Nyamo.