The groups want to stop personal data being passed around without owners being notified or compensated.
Apple is just one of six application makers being pursued by the two groups of consumers.
The legal firm putting together one class action lawsuit said it might also take action against Google over data leaking from Android applications.
Backflip Studios, the Weather Channel, Dictionary.com and others were named in court papers supporting the lawsuits.
The papers allege that many applications collect so much personal data that users can be individually identified. This is despite Apple operating a policy that allows data to be shared with third parties only if an app requires the information to keep running.
The complainants said many firms, including advertisers, were managing to track and identify individuals via the unique device ID Apple assigns to every gadget. Apple does not do enough to enforce its privacy policy or restrict use of unique IDs, they allege.
Apple has yet to respond to requests for comment.
The law firm behind one of the class action lawsuits said it was considering whether to prepare a case against Google, saying that many Android applications leak personal data too.
Despite the filing of separate lawsuits, some experts suggest the court cases will not succeed.
"If this were a major issue, all web browsers would have to shut down and there would not be any advertising on the internet," Trip Chowdhry, Global Equities research analyst, told Reuters.