| Game |
| Result | Moves |
Year |
Event/Locale | Opening |
| 1. A Kveinys vs J Carron |
| 1-0 | 43 |
2004 |
Zürich Meister | E32 Nimzo-Indian, Classical |
| 2. A Kveinys vs Timman |
| ½-½ | 56 |
2004 |
36th Olympiad | E32 Nimzo-Indian, Classical |
| 3. A Kveinys vs Motylev |
| ½-½ | 23 |
2005 |
15th European Team Championship | E58 Nimzo-Indian, 4.e3, Main line with 8...Bxc3 |
| 4. A Kveinys vs M Becker |
| 1-0 | 59 |
2005 |
Open Norwegian Championship | E43 Nimzo-Indian, Fischer Variation |
| 5. A Kveinys vs D Zagorskis |
| ½-½ | 10 |
2005 |
Lithuanian Championship | E59 Nimzo-Indian, 4.e3, Main line |
| 6. A Kveinys vs M Tonndorf |
| 1-0 | 33 |
2005 |
20th North Sea Cup | E38 Nimzo-Indian, Classical, 4...c5 |
| 7. A Kveinys vs E Ovod |
| ½-½ | 44 |
2006 |
Cappelle la Grande | E42 Nimzo-Indian, 4.e3 c5, 5.Ne2 (Rubinstein) |
| 8. A Kveinys vs S Fedorchuk |
| 1-0 | 31 |
2006 |
Polish Team Championship | E32 Nimzo-Indian, Classical |
| 9. A Kveinys vs F Berend |
| ½-½ | 52 |
2006 |
37th Chess Olympiad | E32 Nimzo-Indian, Classical |
| 10. A Kveinys vs A H Wohl |
| 0-1 | 39 |
2006 |
22nd Bad Wörishofen Festival | E32 Nimzo-Indian, Classical |
| 11. A Kveinys vs W Mueller |
| 1-0 | 61 |
2006 |
22nd Bad Wörishofen Festival | E56 Nimzo-Indian, 4.e3, Main line with 7...Nc6 |
| 12. A Kveinys vs M Popovic |
| 1-0 | 35 |
2008 |
Reykjavik Open | E38 Nimzo-Indian, Classical, 4...c5 |
| 13. A Kveinys vs J Parker |
| 1-0 | 65 |
2008 |
Euro Club Cup | E32 Nimzo-Indian, Classical |
| 14. A Kveinys vs J L Hammer |
| 1-0 | 66 |
2008 |
Reykjavik Open | E21 Nimzo-Indian, Three Knights |