  In the present paper, we deal with multiple generalized Genocchi numbers and
polynomials. Also, we introduce analytic interpolating function for the
multiple generalized Genocchi numbers attached to \c{hi} at negative integers
in complex plane and we define the multiple Genocchi p-adic L-function.
Finally, we derive the value of the partial derivative of our multiple p-adic
l-function at s=0.
