TV commercials from US food giant Mondelez and German automaker Volkswagen are the first to be banned under the new British gender stereotypes.
Ban on ads with "harmful sexual stereotypes" or those likely to cause "serious or" widespread criminality "came into effect in June.
The first prohibited ad for Philadelphia cheese showed two dads holding a baby on one
The other, VW ad, showed that men were adventurous while a woman was sitting by a stroller.
Complainants said the advertising had saved a harmful stereotype by claiming to be men could not look after children and be so incompetent that they would endanger young people.  Image copyright
Meanwhile, three people complained about an ad for the Volkswagen eGolf car.
It showed a sleeping woman and a man in a tent on a steep cliff, two male astronauts swimming in a spaceship, and a male paragolf. The athlete makes the long jump before moving on to the last scene where a woman is sitting on a bench next to a stroller.
The complainants alleged that the ad maintained harmful gender stereotypes by showing men performing adventurous activities, as opposed to a woman in a caring role.
Mondelez UK argued that the ad had a positive image of men with a responsible and active role in childcare in modern society. It said it chose to present a pair of dads to avoid a stereotype of new mothers being responsible for children.
ASA said the ad had a light-hearted and funny intent, but she described the men as "a bit unhappy and inattentive." As a result, they were unable to effectively take care of the children. "
The ad stated that men were unable to take care of both children and women, and that fathers had not cared for the children, children were correct because of their gender".
Volkswagen UK said its ad has no indication that childcare is exclusively associated with women, and the fact that the woman is quiet and reading in her advertising may be viewed as a violation of the stereotypical image of harassed or anxious parents in advertising.
ASA said the ad presented gender stereotypes "in ways that are likely to do harm and therefore violate the Code." It was pointed out in advertising that stereotypical male and female roles are associated with only one gender and adventurous activities "with women who appeared to be" passive "or who had a stereotypical role in nursing."
The ASA introduced its ban two months ago because some representations could play a role in "limiting people's potential".
The new rules apply to both broadcast and non-broadcast advertising, including online and social media advertising.