FOR many people, it is the second biggest fear of flying: sitting next to a screaming, kicking, uncontrollable child.

Particularly if that child isn’t theirs.

Next to landing hastily on something other than a runway, sharing the cabin with a fussy toddler is about the worst luck many travelers can imagine. And as the economy and security regulations conspire to squeeze the comforts out of air travel  lines are long, flights are full and increasingly devoid of amenities  the sound of a baby’s wail can be the breaking point for already frayed nerves.

Now, travelers without children are doing some fussing of their own. Some are calling for airlines to implement child-free flights, or designate “family-only” sections on planes, in the wake of some high-profile tantrums.

In July, Qantas settled a lawsuit from a woman who claimed that she suffered hearing loss after sitting next to a screaming 3-year-old boy on a 2009 flight from New York to Australia. (Terms of the settlement were not disclosed.) In January, AirTran removed an entire family from a flight before takeoff from Fort Myers, Fla., because their 3-year-old girl was hitting the parents, making noise and refusing to take her seat. And in March, a 42-year-old woman allegedly grabbed a boy (3 years old, again) for kicking her chair during a Southwest flight to Las Vegas.