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We study multipliers of Hardy-Orlicz spaces $\mH_{\Phi}$ which are strictlycontained between $\bigcup_{p>0}H^p$ and so-called ``big'' Hardy-Orlicz spaces.Big Hardy-Orlicz spaces, carrying an algebraic structure, are equal to theirmultiplier algebra, whereas in classical Hardy spaces $H^p$, the multipliersreduce to $H^{\infty}$. For Hardy-Orlicz spaces $\mH_{\Phi}$ between these twoextremal situations and subject to some conditions, we exhibit multipliers thatare in Hardy-Orlicz spaces the defining functions of which are related to$\Phi$. Even if the results do not entirely characterize the multiplieralgebra, some examples show that we are not very far from precise conditions.In certain situations we see how the multiplier algebra grows in a sense from$\Hi$ to big Hardy-Orlicz spaces when we go from classical $H^p$ spaces to bigHardy-Orlicz spaces. However, the multiplier algebras are not always ordered astheir underlying Hardy-Orlicz spaces. Such an ordering holds in certainsituations, but examples show that there are large Hardy-Orlicz spaces forwhich the multipliers reduce to $\Hi$ so that the multipliers do in general notconserve the ordering of the underlying Hardy-Orlicz spaces. We apply some ofthe multiplier results to construct Hardy-Orlicz spaces close to$\bigcup_{p>0}H^p$ and for which the free interpolating sequences are no longercharacterized by the Carleson condition which is well known to characterizefree interpolating sequences in $H^p$, $p>0$.

Pointwise multipliers in Hardy-Orlicz spaces, and interpolation