Television ads from the American food giant Mondelez and German car manufacturer Volkswagen are the first to be banned under new British gender stereotype rules.
Prohibition on ads with "harmful gender stereotypes" or those likely to cause "serious or extensive crimes" entered into force in June.
The first banned ad, for Philadelphia cheese, showed that two fathers left a child on a restaurant conveyor belt.
The second, the VW advertisement, showed that men were adventurous as a woman sat by a stroller.
The complainants said that the advertising defended a harmful stereotype by suggesting that men were unable to care for children and were so incompetent that they put young people at risk.
Meanwhile, three people complained about an advertisement for the Volkswagen eGolf car.
It showed a sleeping woman and a man in a tent in a clean cliff, two male astronauts floating in a spaceship and a male pair of athletes doing the long jump, before cutting to the final scene depicting a woman sitting on a bench next to a stroller.
The complainants said that the ad defended harmful gender stereotypes by showing men engaged in adventurous activities as opposed to a woman in a caring role.
"The code is broken"
Mondelez UK claimed that the ad showed a positive image of men with a responsible and active role in childcare in modern society. It said it chose to present a couple of fathers to avoid a stereotype of new mothers responsible for children.
ASA said the advertisement had an easy-going and comical intention, but portrayed the men as "somewhat unhappy and inattentive, which resulted in them not being able to take care of the children effectively."
It said the ad "relied on the stereotype that men could not take care of children as well as women and suggested that fathers were not able to care for children properly because of their gender. "
Volkswagen UK said that its advertisement did not suggest that childcare was only associated with women , and the fact that the woman in her ad was calm and reading could be seen as contrary to the stereotypical portrayal of harassed or troubled parents in advertising.
ASA stated that the ad presented gender stereotypes "in a way that was likely to cause harm and therefore broke the code."
It said by compiling images of men "in extremely ordinary environments and conducting adventurous activities" with women who appeared "passive or engaged in a stereotypical caregiving role", the advertisement had suggested that stereotyped male and female roles were exclusively associated with a gender.
ASA introduced its ban two months ago because it showed that certain plays could play a role in "limiting people's potential".
The new rules include both broadcast and non-broadcast ads, including online and social media.