It was a day of differing fortunes for the Israelis competing in the first round at the Australian Open on Monday. Shahar Pe'er and Dudi Sela advanced to the round two, but Tzipi Obziler and Harel Levy were already sent packing after the first day of the tournament in Melbourne. Pe'er, who is ranked No. 17 in the world, won the first set against Renata Voracova (107) 6-2, but got herself into a little trouble after dropping the second set by the same score line. The 20-year-old Israeli, would, however, come back with a vengeance and claimed the third set 6-0 on her way to a second round meeting with Jessica Moore (376). The Australian, who got a wild card to the season's first Grand Slam, surprised American Julie Ditty (101) 6-3, 6-2. "I didn't play well today," Pe'er said on Monday. "The first round is always tough and it takes time to find your rhythm. I'm happy I won as that was the goal and I hope to improve with every round I play. "I improved my play in the third set. I was aggressive and I mixed up my shots. There were a lot of Israelis and Jews in the crowd and I really enjoyed playing in front of them. I have a rest day on Tuesday and I will train and prepare for the next round." Reflecting on her upcoming match, Pe'er added: "I don't know much about Moore, but I'll speak to some of the other players and coaches and try and collect as much as information as possible." Sela (66) cruised to the second round on Monday, defeating Austrian qualifier Martin Slanar (277) 6-2, 6-4, 6-2. The Israeli broke in the first game of the match and was comfortably ahead throughout the encounter. Next up for Sela is a far tougher challenge in the figure of Ivo Karlovic. The giant Croatian (2.08 meters) defeated Britain's Jamie Baker 6-4, 6-4, 6-7 (1), 6-4. Harel Levy (160), who came through three rounds of qualifying to reach the main draw, stumbled at the first hurdle on Monday, losing 6-4, 6-2, 6-1 to Italian Andreas Seppi (48). Levy got off to an outstanding start, breaking twice and taking a 4-0 lead. But he lost the next nine games on the trot and fell into a deficit from which he could not recover. Obziler (81) was a massive underdog against 11th seed Elena Dementieva and unsurprisingly lost 6-2, 6-2 to the Russian on Monday. Dementieva claimed the first five games of the match and is on course to face Pe'er in the third round of the tournament. On Tuesday, Evgenia Linetskaya (584), who reached the fourth round of the Australian Open in 2005 as a Russian, will play Luxembourg's Anne Kremer (84) in the first round in what will be her first appearance on tour as an Israeli.