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An allegation (also called adduction) is a claim of a fact by a party in a pleading, which the party claims to be able to prove. Allegations remain assertions without proof, until they can be proved.
There are also marital allegations: marriage bonds and allegations exist for couples who applied to marry by licence. They do not exist for couples who married by banns. The marriage allegation was the document in which the couple alleged (or frequently just the groom alleged on behalf of both of them) that there were no impediments to the marriage.
Generally, in a civil complaint, a plaintiff alleges facts sufficient to establish all the elements of the claim and thus states a cause of action. The plaintiff must then carry the burden of proof and the burden of persuasion in order to succeed in the lawsuit.
Disjunctive allegations 
Disjunctive allegations are allegations in a pleading joined together by an "or". In a complaint, disjunctive allegations are usually per se defective because such a pleading does not put the party on notice of which allegations they must defend.
On the other hand, defendants often plead in the alternative by listing seemingly inconsistent defenses. For example, "I did not do the crime", "if I did, I didn't know", or "even if I did know, I've got a good excuse". Such a pleading may be considered disjunctive and may be permissible. Allegation is always in plural.
See also 
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