A number of them are falling foul of UK advertising codes by carrying messages that could appeal to young people aged under 18, the survey found.
However, the ASA has given an almost clean bill of health to the online sector, claiming only 1 per cent of its ads contravene the codes.
The verdict follows a six-month survey by the ASA - the first of its kind - covering 354 banner and 258 pop-up ads that appeared on a range of UK websites between July and December last year.
Only one banner ad - for a car - broke the rules and had already had complaints about it upheld by the ASA.
The watchdog said most banner and pop-up ads were unlikely to provoke an ASA investigation because they contained only simple messages.
Thirty-seven ads were deemed "questionable" by researchers, mostly because they included price or other claims needing to be supported by evidence, or had appeared on inappropriate websites.
Danny Meadows-Klue, the chief executive of the Interactive Advertising Bureau, claimed the survey confirmed the industry's commitment to self-regulation. But he warned: "We can't afford to rest on our laurels."