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In p-hemiregular hemirings, some properties of 'prime fuzzy p-ideals' are examined. In the case of fuzzy p-ideal, p-hemiregular hemiring is also characterised. It is showed that in the case of hemiring H, fuzzy subset ϕ is a 'prime fuzzy left p-ideal' in H if and only if ϕ is having two values, set having all values ofǐ in H so that ϕ(p) equals to one is a 'prime left(right) p-ideal' in H, ϕ(0) = 1. In hemirings for 'maximal fuzzy left(right) p-ideals', some related properties are also studied.