У роботi розглядається багаточастотна система iз лiнiйно перетвореними аргументами запiзнюючого типу. Для повiльних змiнних задано багатоточковi умови, решта умов iнтегральнi i заданi на двох промiжках iз промiжку $[0,L]$ визначення системи рiвнянь. 

Усереднення за швидкими змiнними здiйснено як у системi рiвнянь, так i в iнтегральних умовах. Доведено iснування єдиного розв’язку усередненої i точної задач. Одержано, явно залежну вiд малого параметра, оцiнку похибки методу усереднення.

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