In this paper we present some new identities for multiple polylogarithms (abbr. MPLs) and harmonic star sums MHSSs) by using the methods of iterated integral computations logarithm functions. Then, applying these formulas obtained, establish explicit relations between Kaneko-Yamamoto type zeta values K-Y MZVs), MZVs) MPLs. Further, find MZVs MZSVs). Furthermore, define an Apéry-type variant MZS...