  In the present paper we continue the project of systematic construction of
invariant differential operators on the example of the non-compact exceptional
algebra $E_{7(-25)}$. Our choice of this particular algebra is motivated by the
fact that it belongs to a narrow class of algebras, which we call 'conformal
Lie algebras', which have very similar properties to the conformal algebras of
$n$-dimensional Minkowski space-time. This class of algebras is identified and
summarized in a table. Another motivation is related to the AdS/CFT
correspondence. We give the multiplets of indecomposable elementary
representations, including the necessary data for all relevant invariant
differential operators.
