A right ideal I of a ring R is local if \(x\in R\), \(\{x_ 1,...,x_ n\}\subseteq I\) and \((x-x_ 1)R(x-x_ 2)...(x-x_{n-1})R(x-x_ n)=0\) imply that \(x\in I\), and an ideal P of R is pseudoprime if P contains a prime ideal of R. A ring R is normal if x,y\(\in R\) and \(xRy=0\) imply that \(ann(x)+ann(y)=R\), and R is neocommutative if the product of any two finitely generated ideals is finitely generated. The following results are established: if R is a neocommutative ring with identity then (a) an ideal of R is local if and only if it is an intersection of pseudoprime ideals, and (b) if R is normal, then every right ideal is local, and if R is commutative and every principal ideal of R is local, then R is normal. These results generalize results established by \textit{J. C. Dyre} [Math. Scand. 50, 44-54 (1982; Zbl 0468.46016)]. Our assumption that R be neocommutative has been relaxed by \textit{G. Mason} and \textit{R. Raphael} [A propos des ideaux locaux: corrigendum et addendum, Ann. Sci. Math. Qué. (to appear)].