A usually secretive or illicit sexual relationship WordNet 3.0 & Open English WordNet

An affair is a sexual relationship, romantic friendship, or passionate attachment in which at least one of its participants has a formal or informal commitment to a third person who may neither agree to such relationship nor even be aware of it. Wikipedia

Sexual relationship, romantic friendship, or passionate attachment between two people without the attached person's significant other knowing. Wikipedia Disambiguation

A sexual relationship or a romantic friendship or passionate attachment between two people Wikipedia Disambiguation

Secretive sexual and usually adulterous relationship between two people Wikidata

A love relationship. OmegaWiki

A romantic relationship with someone who is not one's regular partner (boyfriend, girlfriend). Wiktionary

A love affair. Wiktionary

An illicit sexual relationship or affair. Wiktionary