Let R be a commutative ring and M be a unital R-module. A submodule L of M is called an essential submodule of M, if  for any nonzero submodule K of M. A submodule N of M is called an e-small submodule of M if, for any essential submodule L of M,  implies  An R-module M is called an e-small monoform if, for each nonzero submodule N of M and for each nonzero  is e-small in N. In this paper, we introduce the concept of e-small monoform modules as a generalization of monoform modules, and give some of their properties, characterizations and examples.

On the other hand, we study the relations between e-small monoform modules and other related modules.

small submodules, e-small submodules, monoform modules, e-small monoform modules.