Apple has slapped Motorola with a countersuit over six of its multi-touch patents.

In two complaints filed with the Wisconsin Western District Court, Apple claimed several of Motorola’s smartphones, including the Droid, Cliq, BackFlip and Devour, violate six of its patents covering aspects of multi-touch technology used in touchscreens.

Apple asked the court to enjoin Motorola from further infringing its patents, and also requested the court award three-fold damages allowed under patent law when infringement is deemed willful and deliberate.

Apple provided the court with extensive documentation on the first patent in question, No. 7,479,949, with its accompanying exhibit weighing in at 362 pages. Exhibits on the other patents ranged from five pages to 82 pages.

Motorola said it had not yet reviewed the counterclaims and declined to provide specific comments on Apple’s lawsuit, but a spokeswoman said the company intended to “vigorously defend ourselves in this matter. We are confident in our position and will pursue our litigation to halt Apple’s continued infringement.”

Apple’s suit comes less than a month after Motorola filed a complaint with the U.S. International Trade Commission (ITC) and two U.S. courts claiming the iPhone maker violated 18 of its patents on early stage innovations in cellular technology, including W-CDMA, GPRS, 802.11, antenna design and key smartphone technologies, including wireless email, proximity sensing, software application management, location-based services and multi-device synchronization.

The countersuit ratchets up heated legal battles over wireless technology. Apple and HTC are already fighting over patents, and Apple also has filed a complaint with the ITC against Nokia. Motorola is being sued by Microsoft over Android, and the operating system itself is the center of a heated fight between Oracle and Google over Java.