2010-11: Arkhip Nekolenko skated for Krylya Sovetov's 1995 and 1996-born squads and played for CSKA's U16 team in the Russian championships. He also represented Moscow in the 2010 U15 tournament. In 20 games with the 1995 squad he scored 11 goals with 17 assists and 4 penalty minutes. Nekolenko played eight games for the 1996 squad and had 10 goals with 5 assists. In five games with CSKA he scored 5 goals with 1 assist and was +1. He scored 1 goal with 4 assists and was +3 in five games for Team Moscow.
2011-12: Nekolenko played for Krylya Sovetov's 1995-born team in Moscow; scoring 16 goals with 17 assists. He represented Russia in the 2012 U16 Youth Olympic Games and scored 1 goal with 3 assists — finishing +6.
2012-13: Nekolenko skated in Russia's U22 MHL as a 16-year-old and represented Russia in three international tournaments. He scored 11 goals with 11 assists and was +5 with 18 penalty minutes in 41 MHL regular season games for MHC Spartak and was +2 with 1 goal, 1 assist and 4 penalty minutes in six playoff games. Nekolenko scored 1 goal in four games for Russia at the 2012 U19 World Hockey Challenge in Canada. Playing for the U17 team he scored 2 goals with 1 assist and was +4 in four games at the Five Nations Tournament in Russia and was +1 with no points and 2 penalty minutes in three games at the 2013 Winter Youth Olympic Festival.
2013-14: Nekolenko returned to MHC Spartak for his second MHL season. Nekolenko was ranked seventh amongst European skaters in Central Scouting's mid-term rankings prior to the 2014 NHL Draft.
Nekolenko is a very interesting player with great skating and good puckhandling skills. He is a player who can score and pass the puck, but is mainly a goal-scorer. Gifted with a great shot, he can beat the goalie in a variety of ways. He usually plays the off-wing and can be very dangerous when the ice opens up and he has time with the puck on his blade. Nekolenko can become a very good goal-scorer, but needs to bulk up and get some consistency.