  An adjoint pair is a pair of densely defined linear operators $A, B$ on a
Hilbert space such that $\langle Ax,y\rangle=\langle x,By\rangle$ for $x\in
\cD(A), y \in \cD(B).$ We consider adjoint pairs for which $0$ is a regular
point for both operators and associate a boundary triplet to such an adjoint
pair. Proper extensions of the operator $B$ are in one-to-one correspondence
$T_\cC\leftrightarrow \cC $ to closed subspaces $\cC$ of
$\cN(A^*)\oplus\cN(B^*)$. In the case when $B$ is formally normal and
$\cD(A)=\cD(B)$, the normal operators $T_\cC$ are characterized. Next we assume
that $B$ has an extension to a normal operator with bounded inverse. Then the
normal operators $T_\cC$ are described and the case when $\cN(A^*)$ has
dimension one is treated.
