But deep rivalries between their two main factions, which in the past led to civil war, could wreck an alliance that over the last decade has put semiautonomous Iraqi Kurdistan on the threshold of statehood.
"The alliance at the base of Iraq's Kurdistan Regional Government is straining amid mounting regional tensions," the U.S. global security consultancy Stratfor.
"The underlying rifts between the two parties will widen as a broader competition intensifies between Turkey and Iran."
As has happened in recent decades, Iraq's neighbors, with restive Kurdish minorities of their own, have encouraged the differences between the Kurdistan Democratic Party and the Patriotic Union of Kurdistan to ensure that no independent Kurdish state emerges in Iraq.
Iraq has some 4.5 million Kurds but there are another 25 million spread over Turkey, Iran and Syria.
Stratfor noted that "in these tougher times, the cohesion of the KRG will be tested" as competing outside powers seek to exploit the divisions between the KDP, led by Massoud Barzani, currently president of the Kurdistan Regional Government, and the PUK, headed by Iraqi President Jalal Talabani.
The PUK draws its strength from the urban left in Kurdistan's secular southwest bordering Iran, with which Talabani has frequently allied himself.
The KDP is more tribal and conservative, long dominated by the Barzani family whose iconic patriarch Mullah Mustafa, Massoud's late father, waged a separatist guerrilla war against Baghdad from the 1950s.
The party controls the northwest of mountainous Kurdistan, which borders Turkey, long hostile to the Iraqi Kurds but now their unlikely ally.
The December incapacitation of Talabani, elected Iraq's president after the U.S.-led invasion of 2003 that toppled Saddam Hussein, has heightened the sense of crisis not just in Kurdistan, but in Iraq as a whole.
Talabani, 79, was laid low by a stroke that probably has put an end to his political career.
This has weakened the PUK at a critical time, when the Kurds' 2005 power-sharing agreement in the three provinces that make up Iraqi Kurdistan is up for renegotiation.
The PUK wants to renew the agreement, which gave the parties equal power in the KRG. But the Barzani clan's been extending its control at the PUK's expense and that's likely to be stepped up now that Talabani's out the frame.
For years he's been the great facilitator of Iraq's turbulent politics, containing the growing rift between the KRG and the Baghdad government of Prime Minister Nouri al-Maliki, over land and especially control of Kurdistan's oil reserves of 45 billion barrels, the key to its independence.
The possibility of Iraq fracturing has thus increased and the Kurdish factions are looking toward old enemy Turkey, which has offered to build pipelines to transport the KRG's oil and gas exports to the Mediterranean, bypassing Baghdad's control.
Over the years, the two Kurdish parties, each with their armies of turbaned fighters known as peshmerga -- "those who face death" -- found it expedient to forge alliances with Turkey or Iran.
In the 1980-88 Iran-Iraq war, the KDP was backed by Iran, the PUK by Saddam, which showed how far Talabani was prepared to go to seek supremacy of Kurdistan. They reached a tenuous truce in 1986. But in 1994, just two years after the KRG was formed under U.S. auspices, full-scale civil war erupted.
The parties reunited after the Americans toppled Saddam. That alliance has held for a decade.
That it's splintering now is due in part to the emergence of a third Kurdish party, Goran, formed in 2009 by Kurds fed up with both the PUK and the KDP.
"With Kurdish politics in such flux," Stratfor observed, "neither party cares to test the voters' will in fresh elections. In June, provincial elections were delayed for the fourth time -- this time indefinitely."
Veteran Iraqi analyst Salah Nasrawi says Talabani's departure from the political arena will unravel the "package of powers" exercised by Talabani, Maliki and Barzani in recent years.
"If one of the three figures in the package disappears, the package has to be renegotiated," he explained. "It will be nearly impossible to replace Talabani."
If he dies, the PUK and KDP will be plunged into a power struggle that will destabilize an already shaky Iraq.