  We study analytic properties of multiple zeta-functions of generalized
Hurwitz-Lerch type. First, as a special type of them, we consider multiple
zeta-functions of generalized Euler-Zagier-Lerch type and investigate their
analytic properties which were already announced in our previous paper. Next we
give `desingularization' of multiple zeta-functions of generalized
Hurwitz-Lerch type, which include those of generalized Euler-Zagier-Lerch type,
the Mordell-Tornheim type, and so on. As a result, the desingularized multiple
zeta-function turns out to be an entire function and can be expressed as a
finite sum of ordinary multiple zeta-functions of the same type. As
applications, we explicitly compute special values of desingularized double
zeta-functions of Euler-Zagier type. We also extend our previous results
concerning a relationship between $p$-adic multiple $L$-functions and $p$-adic
multiple star polylogarithms to more general indices with arbitrary (not
necessarily all positive) integers.
