  Several results concerning multipliers of symmetric Banach function spaces
are presented firstly. Then the results on multipliers of
Calder\'on-Lozanovskii spaces are proved. We investigate assumptions on a
Banach ideal space E and three Young functions \varphi_1, \varphi_2 and
\varphi, generating the corresponding Calder\'on-Lozanovskii spaces
E_{\varphi_1}, E_{\varphi_2}, E_{\varphi} so that the space of multipliers
M(E_{\varphi_1}, E_{\varphi}) of all measurable x such that x,y \in E_{\varphi}
for any y \in E_{\varphi_1} can be identified with E_{\varphi_2}. Sufficient
conditions generalize earlier results by Ando, O'Neil, Zabreiko-Rutickii,
Maligranda-Persson and Maligranda-Nakai. There are also necessary conditions on
functions for the embedding M(E_{\varphi_1}, E_{\varphi}) \subset E_{\varphi_2}
to be true, which already in the case when E = L^1, that is, for Orlicz spaces
M(L^{\varphi_1}, L^{\varphi}) \subset L^{\varphi_2} give a solution of a
problem raised in the book [Ma89]. Some properties of a generalized
complementary operation on Young functions, defined by Ando, are investigated
in order to show how to construct the function \varphi_2 such that
M(E_{\varphi_1}, E_{\varphi}) = E_{\varphi_2}. There are also several examples
of independent interest.
