A double-marking language is one in which the grammatical marks showing relations between different constituents of a phrase tend to be placed on both the heads (or nuclei) of the phrase in question, and on the modifiers or dependents.
For example, in Turkish, in a genitive construction involving two definite nouns, both the possessor and the possessed are marked, the former with a suffix marking the possessor (and corresponding to a possessive adjective in English) and the latter in the genitive case.
For example, 'brother' is kardeş, and 'dog' is köpek, but 'brother's dog' is kardeşin köpeği.
Another example is a language in which endings that mark gender or case are used to indicate the role of both nouns and their associated modifiers (such as adjectives) in a sentence (such as Russian and Spanish) or in which case endings are supplemented by verb endings marking the subject, direct object and/or indirect object of a sentence.
Proto-Indo-European had double-marking in both verb phrases (verbs were marked for person and number, nominals for case) and noun-adjective phrases (both marked with the same case-and-number endings) but not in possessive phrases (only the dependent was marked).