Abstarct: At first we recall the notions of zero- product preserving maps, jordan zero-product preserving maps and Lie zero-product preserving maps. Then we generalize the above mentioned notions as strongly zero-product preserving maps, strongly Jordan zero-product preserving maps and strongly Lie zero-product preserving maps on arbitary normed algebras . we invstigate these notions on certain normed algebras induced by a non-zero normed vector space and a non –zero bounded linear functional . also we present some hereditary properties concerning these notions,such as the direct product, the composition and the tensor product of two maps,Finally we discuss about the second dual and also some miscellaneous properties of these maps.