It surrounds in-app purchasing, whereby users buy virtual currency and add-ons costing up to £70 for games or other software. Apps that use the system are often free to download initially.
The parents argue that Apple made it too easy for children to spend on digital items such as “smurfberries” in the game Smurfs Village without the "authorisation of their parents".
The in-app purchases are billed to the iTunes account and credit card associated with the iPhone or iPad. Several incident shave been reported of children running up hundreds of pounds in charges, in both Britain and the United States.
In their court filing, the American parents accuse Apple of “inducing” children to make in-app purchases.
“Among the many thousands of apps that Apple offers for sale are gaming apps aimed at children,” it says.
“Many such games are designed to induce purchases.”
“These games are highly addictive, designed deliberately to be so, and tend to compel children playing them to purchase large quantities of game currency, amounting to as much as $100 per purchase or more.”
In its attempt to have the case thrown out, Apple highlighted controls in iOS that allow parents to restrict in-app purchasing. According to the parents however, until recently they were not strong enough.
The US Federal Trade Commission is investigating in-app purchasing after complaints from Congressman Edward Markey.
“We fully share your concern that consumers, particularly children, are unlikely to understand the ramifications of these types of purchases," the regulator’s chairman Jon Leibowitz said last year.
Apple has not publicly commented on the class action against it.