Abstract. It is proved that --- under certain conditions --- solutions $f$ of the functional equation $$ f(x)=h(x,y,f(g_1(x,y)),\ldots,f(g_n(x,y))), (x,y)\in D\subset{{\msbm R}^n}\times{\msbm R}^l $$ having Baire property are continuous, even if $1\le l\le n$. As a tool we introduce new function classes which --- roughly speaking --- interpolate between Baire property and continuity.

AMS Subject Classification (1991): 39B05, 54E52

Received August 12, 1999, and in revised form April 5, 2000. (Registered under 2753/2009.)