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VI. ELIGIBILITY OF PLAYERS AND CAPTAINS
35. ELIGIBILITY TO REPRESENT A NATION
A player or captain is entitled to represent one nation only at senior professional international level.
Any tennis player who is in good standing with his National Association in accordance with Appendix D shall be qualified to represent that nation as a player or captain if he:
(a)
(i) Is a citizen of that nation and has held a current valid passport of that nation
for a minimum of two years (24 months ) or;
(ii) Is a citizen of that nation, but in circumstances where that nation does not issue its own passport has held a qualifying passport issued by or on behalf of that nation for a period of two years (24 months) which confirms the player’s place of birth as that nation or;
(iii) If after a consecutive period of five years (60 months) residence in that nation can provide a genuine reason for being unable to hold or make application to hold a current valid passport where:
(a) he was born, or has a parent or grandparent born in that nation; or,
(b) he has obtained or procured the right to remain permanently or has been granted humanitarian protection in that nation.
If a player is qualified under this sub section to represent more than one nation and the National Association of one of those nations
wishes to nominate him to represent it, that Association must submit an application to the ITF Executive, who will forward a copy to any other National Association concerned, which shall be entitled to comment within 15 days of receipt. The initial application must be received by the ITF Executive at least three months prior to the event for which the player wishes to be nominated.
The ITF Executive will give a ruling having taken into account all relevant matters.
(b)
(i) A player who has represented, or has been eligible to represent a nation and such a nation is divided into two or more nations, shall immediately be eligible to represent any one of those nations.
(ii) A player who has represented, or has been eligible to represent a nation and such nation is absorbed in whole or in part by another nation, shall immediately be eligible to represent such other nation.
(...)
from:
http://www.daviscup.com/en/organisation/rules-regulations.aspx