The suit, filed in a United States district court, seeks $315 million in deposits, compensation for artwork and gold held in a safe deposit box and unspecified damages from UBS and Credit Suisse.
The plaintiffs accuse the banks of refusing them access to records relating to accounts and a safe deposit box they say their relatives opened in the late 1930s, as conditions for European Jews grew increasingly perilous.
The defendants have "continued to interfere with and conspire against depositors' rights by refusing access to all available records and databases and by refusing to use recommended state-of-the-art technology that would provide greater accuracy in matching names and account numbers," said a statement distributed by the lawyers outside UBS' annual shareholders' meeting
Thursday in Zurich.
Swiss banks paid out $1.25 billion in 1998 to settle claims by Holocaust survivors and the descendants of Holocaust victims whose families held Swiss accounts before and during World War II.
But the two families in the lawsuit -- which also names as defendants the Swiss Bankers Association, the Swiss Federal Banking Commission and Switzerland as a whole -- had their cases rejected by the claims resolution tribunal established to oversee the funds, which said they had insufficient evidence.
Both families base their claims on handwritten records handed down across generations.
One family, the descendants of Mozes Fleishmann, said the Hungarian businessman wrote details about three Swiss accounts holding $2.8 million on a piece of paper and gave it to his 11-year-old son, who survived the war and emigrated to Israel.
The other, the descendants of Paulina Grunfeld and her cousins, said the Romanian department store magnates had Swiss accounts worth more than one million dollars and a large safe deposit box containing artwork, silver and gold.
The suit says Paulina burnt the records on the accounts while in hiding in Romania, but wrote the details in a code disguised as a recipe that she gave to her son Moshe.
UBS said the claims were baseless and pledged to defend itself "vigorously".
"The claims resolution tribunal has repeatedly and thoroughly examined the claims," it said in a statement.
"Neither (the tribunal)... nor UBS found any indication of the existence of the alleged accounts and safe deposit boxes. The US court determined that the information provided by the claimants did not provide sufficient substantiation of their allegations."
The attorneys bringing the suit include US lawyer Ed Fagan, who represented victims in the 1998 settlement. Fagan, who was accused of using victims to maximise his own fees, earned global notoriety for his high-profile handling of the case.