Call it sports labor’s disharmonic convergence.

After suffering only one labor stoppage in the last 10 years, the major American sports leagues are headed into a time of unprecedented uncertainty. Each is dealing with its own complex set of issues between owners and players, including some points that have been controversial nearly from the day the previous collective-bargaining agreements were signed.

And all of the leagues are dealing with an economy that has proved to be the worst in more than a generation and has affected nearly every corner of the business.

On top of that comes something no one at the four leagues or the four unions can remember happening before, the equivalent of a full solar eclipse on the sports-labor calendar: All four major team sports have collective-bargaining agreements expiring in the same year, 2011.

It adds up to a lot of unknowns. A series of interviews by Sports Business Journal with top negotiators on both sides of the table in all four sports reveals hope from all of them that deals can get done, as well as frank acknowledgments that there could be a work stoppage in at least one of the sports.

The commissioners and some team owners in the NFL and NBA, both of which have begun formal bargaining, have made it clear that they are looking for changes in their salary-cap systems, which regulate what they pay their most critical employees, their players. Those on the labor side of the table say major changes typically mean major concessions.

In the NHL, players are unhappy with the CBA they ratified in order to end the 2004-05 lockout. And despite numerous concessions from players, NHL owners are not entirely satisfied with it either.

In Major League Baseball, the MLB Players Association is investigating whether owners colluded to drive salaries down in the last free-agent market. Both union and league officials say it is too early to say what will happen in 2011.

“We could have peace in all of them,” said Bob Batterman, who serves as outside labor counsel to the NFL and NHL as a partner at the powerful Proskauer Rose law firm. “We could have war in all of them, [although] I think that is very unlikely.”

But the heads of the two unions that have begun negotiations, NFLPA executive director DeMaurice Smith and National Basketball Players Association executive director Billy Hunter, both say they believe owners may be preparing to lock their members out.

“I have been through the lockout,” Hunter said. “I can see a fight coming into this one. I don’t want it. But you play the hand that is dealt to you.”