The Mississippi Supreme Court is refereeing a dispute between a Wilkinson County couple and ExxonMobil Corporation over an alleged alligator infestation, with justices scheduled to hear oral arguments Tuesday.

The dispute involves more than 80 alligators that Tom Christmas and his wife argue they didn't discover on land next to their homestead until four years after they bought the property in southwest Mississippi.

The Christmases bought 35 acres between Centreville and Woodville in December 2003. The land had previously been used for hunting and timber and was not occupied when they bought it. Court records do not show from whom they bought the land, but it was not owned by ExxonMobil.

The property was originally operated by Rogers Rental and Landfill Company Inc. The property has 19 rainwater retention ponds, totaling about 85 surface acres of water. Alligators were allegedly introduced to the site from Louisiana as "canaries" to warn of hazardous contamination in the retention ponds. Exactly who put the reptiles there is a matter of dispute.

ExxonMobil has owned the facility since July 2001, but it had a close relationship with Rogers that stretched back to at least 1980. At some point in the 1990s, Rogers stopped accepting new refinery waste, and the facility has since been maintained as a former waste disposal site.

ExxonMobil said the Christmases' real estate agent told the couple about the alligators as far back as 2003. ExxonMobil said that the Christmases waited too long to file a lawsuit saying the alligators robbed them of enjoyment of their land and that the statute of limitations has passed.

ExxonMobil appealed a state Court of Appeals ruling in May that returned the case to Wilkinson County for trial.

The Christmases argue the alligator infestation of the ExxonMobil property is a non-abatable nuisance that has caused a permanent injury to their property. They are seeking damages for permanent depreciation of their land, not an abatement of the nuisance or damages for the temporary loss of use or enjoyment of the property.

The Christmases sued Exxon in August 2008, seeking damages for permanent depreciation of their land. Circuit Judge Lillie Sanders threw out the lawsuit in 2011.

ExxonMobil attorneys said the Christmases should have investigated the alligator issue when they first saw one in 2003.

ExxonMobil argues its hands are tied when it comes to the alligators because they are protected and regulated by the Mississippi Department of Wildlife, Fisheries and Parks.

In a brief, the MDWFP said that under state law only it can decide whether an alligator is a nuisance and only its officers can take steps to move or otherwise deal with them.

ExxonMobil said it cannot be held liable for legally protected wild alligators that allegedly roamed from their property onto the Christmases' adjoining property.

In court documents, the MDWFP said in 2007 it was called upon to address the alleged "infestation" of wild alligators. The department said it counted about 84 alligators on the ExxonMobil land. MDWFP officials said not all may have been counted.

At ExxonMobil's request, MDWFP said it removed seven adult alligators from the property in July 2008.

MDWFP attorneys said the Christmases were not satisfied with what wildlife officers did and sued ExxonMobil.

Attorneys representing the Christmases argue that determining whether the alligators are a nuisance is an issue for a jury. They said the Christmases discovered the alligators when they moved to the property in 2007 and Tom Christmas was allowed on the ExxonMobil property to search for a lost hunting dog.