Research In Motion (RIM) and Motorola have launched dueling patent infringement suits, over technology used in each other’s handsets.

RIM, which filed its suit in U.S. District Court for the Northern District of Texas, claims that Motorola has refused to pay royalties for a number of its patents and that it charges “exorbitant” licensing fees for its technology.

Motorola has responded to RIM’s suit by saying that the company’s claims are “entirely without merit” and that it intends to “vigorously” defend itself against the allegations.

Meanwhile, the ailing U.S. handset maker said it has filed two lawsuits against the BlackBerry maker, one in Eastern Texas and another in Delaware. Motorola is challenging RIM’s patents and alleges that the Canadian company’s technology infringes on some of its patents.

Motorola and RIM had a technology licensing agreement in place since 2003,  but that contract expired at the end of 2007 and the two have failed to agree on new terms.