The main objective of this paper is to study about the action of generalized derivations on prime ideals of an arbitrary ring with involution. In particular, apart from proving some other results, we establish that if
(
F
,
d
)
(F,d)
is a generalized derivation of
R
R
satisfying the condition
[
F
(
x
)
,
x
∗
]
∈
P
[F(x),x^*]\in P
for all
x
∈
R
x\in R
, then one of the following holds:
c
h
a
r
(
R
/
P
)
=
2
char(R/P)=2
,
R
/
P
R/P
is a commutative integral domain,
F
(
R
)
⊆
P
F(R)\subseteq P
.