Reducing noise emission from jet is a major topics of aeroacoustics. Recently, it has been shown that the large coherent structures of a turbulent single-stream jet, which are parts of the noise generation mechanisms, can be interpreted as instability of the mean turbulent flow, especially in the region of the potential core. Reducing noise will be probably only achieved with some new control strategy on the underlying physics of the acoustic wave generation. The present work deals with the last investigations associated to the sensitivity analysis of the single and dual-stream jet instability to any local forcing. Sensitivity is a first step of any aeroacoustic or flow control approach and it is performed by the Parabolized Stability Equations and their adjoint counter part. Validation is first made on a simple semi-analytical supersonic jet. Then sensitivity functions to a source of momentum, mass or energy forcing are given in a supersonic single (M = 1.15) and dual- stream jets (M p = 0.89 and M s = 1.20). The base-flow is obtained from accurate Large Eddy Simulations and included some shock cells. Highest sensitivities are found inside the shear layer close to the external boundary of the potential core and close to the jet inlet, similar to the previous results found in incompressible single stream jet. The growth rate and wave number of the Kelvin-Helmhotz instability and the acoustic (pressure) perturbation are strongly influenced by the shock cell positions