| Game |
| Result | Moves |
Year |
Event/Locale | Opening |
| 1. A Kveinys vs A Petrosian |
| 1-0 | 58 |
1986 |
Sevastopol | B93 Sicilian, Najdorf, 6.f4 |
| 2. Dreev vs A Kveinys |
| ½-½ | 36 |
1986 |
Minsk (Belarus) | A46 Queen's Pawn Game |
| 3. Psakhis vs A Kveinys |
| 1-0 | 29 |
1986 |
Sevastopol | D35 Queen's Gambit Declined |
| 4. A Kveinys vs E Vladimirov |
| 0-1 | 43 |
1988 |
URS Cup rapid | C61 Ruy Lopez, Bird's Defense |
| 5. Karpov vs A Kveinys |
| 1-0 | 20 |
1988 |
Riga | B50 Sicilian |
| 6. A Kveinys vs G Orlov |
| ½-½ | 15 |
1989 |
It (open) | C07 French, Tarrasch |
| 7. A Kveinys vs J Lechtynsky |
| 0-1 | 24 |
1990 |
Rimavska Sobota | B15 Caro-Kann |
| 8. A Kveinys vs W Schmidt |
| 1-0 | 52 |
1990 |
POL-chT | C09 French, Tarrasch, Open Variation, Main line |
| 9. Plachetka vs A Kveinys |
| ½-½ | 37 |
1990 |
Rimavska Sobota | D61 Queen's Gambit Declined, Orthodox, Rubinstein Attack |
| 10. Kupreichik vs A Kveinys |
| 1-0 | 36 |
1990 |
Warsaw | B46 Sicilian, Taimanov Variation |
| 11. V Tukmakov vs A Kveinys |
| ½-½ | 62 |
1990 |
Groningen op | D35 Queen's Gambit Declined |
| 12. A Kveinys vs Stohl |
| ½-½ | 27 |
1990 |
Rimavska Sobota | D91 Grunfeld, 5.Bg5 |
| 13. A Kveinys vs W Schmidt |
| ½-½ | 27 |
1990 |
POL-chT | B40 Sicilian |
| 14. A Kveinys vs Kupreichik |
| 0-1 | 37 |
1990 |
Rimavska Sobota | E70 King's Indian |
| 15. Romanishin vs A Kveinys |
| ½-½ | 26 |
1990 |
Groningen | E04 Catalan, Open, 5.Nf3 |
| 16. K Mokry vs A Kveinys |
| 1-0 | 39 |
1990 |
Rimavska Sobota | C92 Ruy Lopez, Closed |
| 17. A Kveinys vs Kupreichik |
| ½-½ | 38 |
1991 |
Miedzybrodzie | B70 Sicilian, Dragon Variation |
| 18. Petursson vs A Kveinys |
| 0-1 | 40 |
1991 |
It Torcy | D35 Queen's Gambit Declined |
| 19. Wojtkiewicz vs A Kveinys |
| 0-1 | 49 |
1991 |
Poland | E04 Catalan, Open, 5.Nf3 |
| 20. A Kveinys vs Shabalov |
| ½-½ | 13 |
1991 |
Torcy op | C10 French |
| 21. A Kveinys vs W Schmidt |
| 1-0 | 36 |
1991 |
POL-chT | C09 French, Tarrasch, Open Variation, Main line |
| 22. Krasenkow vs A Kveinys |
| ½-½ | 15 |
1991 |
Poland | E00 Queen's Pawn Game |
| 23. A Kveinys vs Balashov |
| ½-½ | 22 |
1991 |
Miedzybrodzie | C92 Ruy Lopez, Closed |
| 24. K Spraggett vs A Kveinys |
 | ½-½ | 65 |
1991 |
Torcy | A00 Uncommon Opening |
| 25. Rublevsky vs A Kveinys |
| ½-½ | 26 |
1992 |
Ostrava | B23 Sicilian, Closed |