Form factors in quantum integrable models with $GL(3)$-invariant $R$-matrix

We study integrable models solvable by the nested algebraic Bethe ansatz and possessing $GL(3)$-invariant $R$-matrix. We obtain determinant representations for form factors of off-diagonal entries of the monodromy matrix. These representations can be used for the calculation of form factors and correlation functions of the XXX $SU(3)$-invariant Heisenberg chain.