Abstract. Let $w$ be a modulus function and $H(w)$ be the corresponding Hardy--Orlicz space. If $\phi $ is a self analytic map of the unit disc, then the linear transformation $C_\phi $ on $H(w)$, defined by $C_\phi f=f\circ\phi $ turns out to be continuous and is called a substitution operator. A characterization of operators which are substitution operators is presented. Quasinorm estimate for $C_\phi $ is given and it is utilized to characterize isometric substitution operators on $H(w)$.

AMS Subject Classification (1991): 47B38, 46A06

Received November 24, 1992 and in revised form June 15, 1993. (Registered under 5564/2009.)