We continue to study $l$-adic iterated integrals introduced in the first part. We shall show that the $l$-adic iterated integrals satisfy essentially the same functional equations as the classical complex iterated integrals. Next we are studying $l$-adic analogs of classical polylogarithms.
"ON $l$-adic iterated integrals, II. Functional equations and $l$-adic iterated polylogarithms." Nagoya Math. J. 177 117 - 153, 2005.