The respective international federations for boxing and gymnastics say they will make individual rulings on the eligibility of Russian athletes for next month's Rio Olympic Games.
The International Olympic Committee opted against a blanket ban on Russia for running a state-sponsored doping programme, and asked each sport to vet their own proposed Russian competitors.
Russia has qualified 11 boxers for Rio, including reigning amateur world champions Vitaly Dunaytsev and Evgeny Tishchenko.
An International Boxing Association [AIBA] statement said: "AIBA has taken note and supports the decision of the IOC Executive Board concerning the participation of Russian athletes in the Olympic Games Rio 2016.
"We are reviewing and analysing, on a case by case basis, the anti-doping record of the 11 Russian boxers currently qualified for Rio 2016. This information and the decision of AIBA in respect of the athlete's eligibility will be submitted to the IOC for confirmation in due course.
"AIBA remains committed to the WADA Code and will deal with any breach of the AIBA Anti-Doping Regulations."
And the Federation Internationale de Gymnastique also said it will "fully adhere" to the IOC's ruling, adding: "The FIG will -- as soon as possible -- establish the "Pool of Russian eligible athletes" ... and will have it verified as requested... then forward it to all concerned parties."
The International Tennis Federation has already said the Russian players nominated for Rio have been subject to a total of 205 drugs tests since 2014, and will be allowed to play.
Cycling's world governing body may follow suit, with president Brian Cookson saying it would be "difficult for us to ban an entire team".
Last month athletics' world governing body the IAAF banned all Russian track and field athletes from international competition unless they could prove they had been comprehensively tested outside Russia -- a decision supported by the IAAF.
Weightlifting is the other sport most likely to issue a blanket ban on Russian competitors in Rio following a significant number of confirmed positive doping tests.
The IOC's decision to pass the decision on to the individual sports' federations has been widely criticised by anti-doping agencies and athletes.
The United States Anti-Doping Agency [USADA] chief executive Travis Tygart said the IOC had missed a chance to assert its leadership and left behind "a confusing mess".
And World Anti-Doping Agency president Sir Craig Reedie said he was "disappointed the IOC did not heed" his organisation's call for a blanket ban.
However, archery has become the latest sport to confirm Russian athletes will be allowed to compete in Rio.
World Archery, the sport's international governing body, said Russia's three qualified archers, Tuiana Dashidorzhieva, Ksenia Perova and Inna Stepanova, have all been "tested extensively" and never previously committed a doping offence.
In a statement, World Archery expressed its "shock and concern" over recent doping revelations but added: "The IOC executive board should be congratulated on its courageous decision not to put a blanket ban on the Russian Federation, which would have been extremely unfair to any clean Russian athlete, who had no part in any of the alleged activities mentioned in the McLaren Report."
