Let
G
=
(
A
∗
B
)
H
G = {(A \ast B)_H}
be the generalized free product of the groups
A
,
B
A,B
amalgamating the subgroup
H
H
, and let
Φ
(
G
)
\Phi (G)
denote its Frattini subgroup. In support of the conjecture that
Φ
(
G
)
⊆
H
\Phi (G) \subseteq H
whenever
G
G
is resiually finite and
H
H
satisfies a nontrivial identical relation, we show, amongst several other things, that the above inequality is indeed valid if in addition at least one of the following holds: (i)
A
,
B
A,B
, each satisfies a nontrivial identical relation; (ii)
G
G
is finitely generated; (iii)
H
H
is nilpotent. In particular (i) completes earlier investigations of the second author. The methods of proof are, however, different.