About Syusuke
Fuji Syusuke (Shusuke), is a third year student at Seishun Gakuen, and is approaching fifteen years of age at the beginning of the series. He is given the title "tensai", or genius, due to his tactical skill on the tennis court.
He is the middle child of the Fuji family. His unnamed father is a foreign-based employee, and is never seen in the series. His mother, 49-year-old Yoshiko, who also has perpetually-closed eyes, is seen in the manga as a kind and dedicated Japanese housewife. His younger brother, Yuuta, is a tennis player at St. Rudolph Middle School. Fuji's elder sister, 24-year-old Yumiko, is considered very attractive and is popular among both Fuji and Yuuta's friends.
Fuji is often seen with a calm and content expression on his face, with his eyes seemingly closed from lightly smiling. However, when he is excited or provoked, or when playing seriously, Fuji reveals his sharp eyes: they are blue in the anime and light brown in the manga.
Fuji is particularly protective of his younger brother Yuuta (probably to make up for former disagreements that almost brought them apart), as displayed throughout the series; he actively tries to "destroy" and punish those who have defeated his younger brother or have made him go through something dangerous (as proved by how differently he treats Jirou Akutagawa from Hyotei and Hajime Mizuki from Saint Rudolph. Though he holds no personal grudge towards Jirou, who won fairly against Yuuta, he does resent Mizuki for a long time after seeing how he treated his brother as someone expendable to ensure his team's victory).
About Yuuta
Yuuta is the younger brother of Shusuke Fuji, who due to their closeness in age always looked out for him while they were younger.
Yuuta was originally a student at Seishun Gakuen, the same school his brother attended, however while he was there, he was constantly living in the shadow of his older brother, and people began referring to him as 'Fuji's Younger Brother'. Because of that, Yuuta didn't join the tennis club during his semester there. However, it was during this period of time that Yuuta went to a private school to learn tennis, and also began resenting his older brother, since he longed for his own identity. While there, he was introduced to Hajime Mizuki, the manager for the St. Rudolph team. Mizuki convinced Yuuta to transfer to St. Rudolph.
In order to make a name for himself, Yuuta decided that it was best to leave and find somewhere else where he would be known for being Fuji Yuuta. He managed to make a name for himself as the Left-hand Killer and Mizuki's best pupil.
After losing to Ryoma Echizen, Yuuta learns that his idol and manager had not told him the truth about his Twist Spin Shot, deliberately not warning him about its flaw and the possible injury he'd sustain. After Fuji utterly defeats Mizuki as a punishment for his mistreatment of Yuuta, he decides to not hold resentment against Mizuki, yet he also asks for permission to seek for his own style. Mizuki allows him to do so, and since then Yuuta and Shusuke's strained relationship has started to mend.
About Syusuke and Yuuta
Syusuke feel for Yuuta a great protective instinct even if Yuuta feel angust by him. So the relationship between them is a mix of love and hate. Kyoudai no kyousou mean "brother(sibling)'s rivalry" for this reason.
info takes from wikipedia