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A left R-module M is called weakly prime module if the annihilator of any nonzero submodule of M is a prime ideal and a proper submodule P of M is called weakly prime submodule if the quotient module M/P is a weakly prime module. This notion is introduced and extensively studied. The module in which, weakly prime submodules and the prime submodules coincide, are studied, and it is shown that multiplicative modules have this property called compatibility property. It is also shown that each R-module is compatible if and only if each prime ideal is maximal or if and only if the R-module R⊕ R is compatible. Over commutative rings the modules in which every proper submodule (proper nonzero submodules) is weakly prime are characterized. It is proved that if dim R<∞, then each R-module has a prime submodule if and only if it has weakly prime submodule.