The charges follow reports that monkey noises were directed by Spain fans at Italy forward Mario Balotelli, and that Russian fans targeted Czech Republic defender Theodor Gebre Selassie. Both players are black.
UEFA said it opened disciplinary cases for "improper conduct of their supporters (racist behaviour, racist chanting)."
The European football body said its disciplinary panel will deal with the cases Thursday.
Spain and Russia will likely receive financial penalties if the cases are proven.
Russia has already been fined €185,000 ($230,000) after being charged by UEFA over its fans' conduct at all three of its group-stage matches in Poland.
UEFA also threatened Russia with a six-point deduction in its 2016 European Championship qualifying group after some of its fans attacked stadium stewards in Wroclaw following the Czech match on June 8. UEFA has said the deduction would be enforced if fans repeated their violent behaviour. The Russian FA has appealed that sanction.
In the first proven case of racist abuse at Euro 2012, UEFA fined the Croatia football association €80,000 ($100,000) for a range of charges including insults directed at Balotelli.
Discrimination monitors appointed by UEFA reported that around 300 Croatia supporters made monkey noises at the Italy forward during a June 14 match in Poznan.
Also Tuesday, UEFA fined Croatia €30,000 ($37,400) after fans displayed "racist banners and symbols" at a June 18 match against Spain in Gdansk. The charges also related to fans who threw fireworks.
A Spanish fans' group previously reported that some Spain followers made monkey noises at Balotelli during a June 10 match in Gdansk. The group, affiliated to the Football Supporters Europe network, said other Spanish fans intervened urging the offenders to stop.
Gebre Selassie acknowledged that he was racially abused by Russians during the opening group match but declined to file a complaint.
UEFA received reports from monitors supplied by FARE, a Europe-wide fans' network, and later asked Czech team officials to help provide evidence which could be used to prosecute the case.
Russian fans displayed "illicit" imperialist flags and set off fireworks at each match, while a fan carrying a national flag aloft ran across the pitch after the match against Poland in Warsaw on June 12.
UEFA pledged a zero-tolerance policy toward combatting racism and discrimination inside Euro 2012 stadiums.
Russia was heavily favoured to advance from Group A but was eliminated as the Czechs and Greece reached the quarterfinals.
On Monday, Russia FA president Sergei Fursenko announced his resignation during a televised meeting with state President Vladimir Putin.
In a second published verdict Tuesday, UEFA fined the Portuguese association €7,000 ($8,750) because a supporter tried to invade the pitch during the quarterfinal victory against the Czechs in Warsaw last Thursday.