The disputes centre on patents held by Qualcomm for technology used in chips in mobile devices such as telephones.
Nokia has for some years paid a licensing fee to Qualcomm under the deal which has just expired. The two companies have not managed to agree a replacement deal.
The just-expired agreement involved the cross-licensing of technology between Qualcomm and Nokia. Nokia has just made a $20 million payment to Qualcomm to cover the second quarter of this year, but Qualcomm has denounced the action, saying that it is not for Nokia to set prices for its intellectual property.
Qualcomm has asked for the American Arbitration Association to arbitrate the dispute and has demanded that Nokia continue to pay it patent licence fees.
In 2005 Nokia and others complained to the European Commission about Qualcomm's behaviour over standardisation for third generation (3G) mobile phone networks. Nokia said that Qualcomm agreed that it would not over-charge for licences to its technology if it was incorporated into industry-wide standards.
Once those standards were set, argued Nokia, Qualcomm levied charges that were excessive and disproportionate. That case is ongoing.
A week later Qualcomm filed a suit in the US alleging that Nokia infringed 11 of its patents. Nokia filed another suit in Europe in recent weeks arguing that the patents on which Qualcomm's cases rest have expired in Europe.
Nokia uses chips from Texas Instruments which, in turn, use technology claimed as its own by Qualcomm. Nokia claims that the Qualcomm patents have expired.