Finland's Nokia says it is suing Apple for breaching 32 technology patents.
Nokia's law suits have been filed in three courts in Germany and one in Texas.
The claims cover patents for displays, user interfaces, software, antennas, chipsets and video coding.
On Tuesday, Apple started legal action against Acacia Research and Conversant Intellectual Property Management, alleging they had conspired with Nokia to extort money from Apple.
Nokia said: "Since agreeing a license covering some patents from the Nokia Technologies portfolio in 2011, Apple has declined subsequent offers made by Nokia to license other of its patented inventions which are used by many of Apple's products."
Between 2009 and 2011 the two companies were locked in a series of tit-for-tat legal battles over the patents for the technology they used in their mobile phones.
At the time Nokia was still the world's leading mobile phone manufacturer, but was being rapidly undermined by the rise of Apple's iPhone.
In the end the two companies settled, with Apple making an undisclosed one-off payment, and making further royalty payments to use Nokia technology.
Nokia eventually sold its mobile phone business to Microsoft in 2014, though earlier this year it said it would re-enter the mobile phone business by licensing its technology and brand name to a new Finish firm called HMD, which is making Nokia-branded phones once more.