Television advertisements from US food giant Mondelez and German carmaker Volkswagen are the first to be banned under new UK gender stereotyping rules.
A ban on ads featuring "harmful gender stereotypes" or those which are likely to cause "serious or widespread offence" came into force in June.
The first banned ad, for Philadelphia cheese, showed two fathers leaving a baby on a restaurant conveyor belt.
The other, VW ad, showed men being adventurous as a woman sat by a pram.
Some 128 people complained to the Advertising Standards Authority (ASA) about the Mondelez advert for its Philadelphia cheese which featured two dads leaving a baby on a restaurant buffet conveyor belt as they were distracted by the food.
Complainants said the advertisement perpetuated a harmful stereotype by suggesting that men were incapable of caring for children and were so incompetent they would place youngsters at risk.
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 sheer cliff face, two male astronauts floating in a space ship and a male para-athlete doing the long jump, before cutting to the final scene showing a woman sitting on a bench next to a pram.
Complainants said that the ad perpetuated harmful gender stereotypes by showing men engaged in adventurous activities in contrast to a woman in a care-giving role.
Gender stereotyping results in "real world harm" says Jess Tye from the @ASA_UK. It's after 2 TV ads have been banned under new UK gender stereotyping rules #r4today https://t.co/qxbb1MgubG pic.twitter.com/1Asqvriap4— BBC Radio 4 Today (@BBCr4today) August 14, 2019
Jess Tye, investigations manager at the Advertising Standards Authority, told the BBC that gender stereotypes in advertising could cause "real-world harms".
"Ads that specifically contrast male and female stereotypes need to be handled with care," she said.
"It's about thinking about what the cumulative effect of those gender stereotypes might be."
Mondelez UK argued 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 feature a pair of fathers to avoid a stereotype of new mothers being responsible for children.
The ASA said the ad had a light-hearted and comical intent, but portrayed the men as "somewhat hapless and inattentive, which resulted in them being unable to care for the children effectively".
It said the ad "relied on the stereotype that men were unable to care for children as well as women, and implied that the fathers had failed to look after the children properly because of their gender".
Volkswagen UK said that its ad made no suggestion that childcare was solely associated with women, and the fact that the woman in its advertisement was calm and reading could be seen as going against the stereotypical depiction of harassed or anxious parents in advertising.
The ASA said the ad presented gender stereotypes "in a way that was likely to cause harm and therefore breached the code."
It said by juxtaposing images of men "in extraordinary environments and carrying out adventurous activities" with women who appeared "passive or engaged in a stereotypical care-giving role", the ad had suggested that stereotypical male and female roles were exclusively associated with one gender.
The ASA introduced its ban two months ago because it found some portrayals could play a part in "limiting people's potential".
The new rules cover both broadcast and non-broadcast adverts, including online and social media.