TORONTO (Reuters) - Canadian zoos may have to curb breeding programs for some rare animals, because a U.S. ban on imports of giraffe, deer and other ruminants means there is no market south of the border for the babies.

The ban on imports of ruminants -- animals with hooves and multiple stomachs -- was imposed last May after a single case of mad cow disease was found on a Canadian farm. Canada responded with similar curbs after a case of the brain-wasting disease showed up on a farm in Washington state in December.

But while Canada allows exceptions to its import ban for rare animals, the United States is keeping its border closed.

"We are not going to breed our (reindeer) until the ban is lifted," the curator of the Assiniboine Park Zoo in Winnipeg, Manitoba said on Wednesday.

Bob Wrigley said the zoo's reindeer herd has risen to 25 from 12, and the zoo expects six more babies to be born in the spring -- animals that under normal circumstances would have found a home in the United States.

"It would be improper herd management to breed them this year," without knowing if they could be sent to other zoos, Wrigley said.

Mark Hemker of the Hemker Wildlife Park in Freeport, Minnesota said he needs the Canadian-bred reindeer to maintain his herd because they are not related to his animals.

The Winnipeg zoo is not worried about its reindeer herd, but says endangered animals which participate in breeding programs around the world must leave Canada to breed because there are no suitable animals at home.

Recognizing the importance of maintaining gene pools and breeding programs for rare and exotic animals, the Canadian Food Inspection Agency has relaxed its import ban for animals headed for zoos and research facilities, and wants its American counterpart to do the same.

"When you have only a few animals left, (they) need to breed," said the food agency's national manager of import and export, Francine Lord. "In the zoo environment, (animals) are in confinement so they will not go into the herd system, they will not go into the feed chain, they will not go anywhere."

The easing of the ban means the Winnipeg zoo can import Alpine ibex and Afghanistan markhors, both goat-like animals, to breed with its very small populations.

But until the U.S. government takes rare and exotic animals off its hit list, the zoo's threatened European bison and endangered South American vicunas will not be able to breed, Wrigley said.

"The ban is not lifted for animals going down (to the United States)," Wrigley said. "We still won't be able to send anything down there."

"Before I came to the zoo, I had no idea how many animals were traveling internationally."