  In this paper, we study the average behaviour of the coefficients of triple
product L-functions and some related L-functions corresponding to normalized
primitive holomorphic cusp form $f(z)$ of weight $k$ for the full modular group
$SL(2,\ \mathbb{Z}).$ Here we call $f(z)$ a primitive cusp form if it is an
eighenfunction of all Hecke operators simultaneously.
