The aim of this work of thesis is the investigation of axion-like particles (ALPs) signatures in the spectra of Active Galactic Nuclei (AGN), in the very-high-energy (VHE, E > 100GeV) -ray range. ALPs, which are candidates for Dark Matter, in the presence of strong magnetic fields could interact with the rays emitted by AGNs, and this effect could be observed in the VHE -ray spectra under the form of "wiggles" or oscillations. Here, the search for ALPs was performed on MAGIC (Major Atmospheric Gamma-ray Imaging Cherenkov) data of the AGN NGC 1275, located in the Perseus cluster. 54:1 hours of MAGIC data have been analysed. The conversion probability of rays in ALPs (P) has been calculated for several values of the mass of ALPS (ma) and coupling (ga). A study of the parameter space for those two quantities has been performed. We found three different states of the source which correspond to flaring, active and low activity state, respectively. Data from the flaring state were used for the search of ALPs signatures. The spectrum is stable in the energy range 50 GeV - 700 GeV, with an integral flux of (8:53 0:24) 10􀀀10 cm􀀀2 s􀀀1 above the energy of 100 GeV. The spectrum can be described by a power-law with an exponential cut-off (EPWL) with 􀀀 index -2.4. In the study of ALPs parameters space, parameters combinations are narrowed down to 10 sets each with several possibilities of ma and coupling ga. Those sets are named S1 - S10 and the corresponding values of ma and ga are in the ranges 90 neV - 110 neV and 0:3 10􀀀11 GeV􀀀1 - 0:5 10􀀀11 GeV􀀀1, respectively. Using each set separately, the convolution of P with the EPWL fit was calculated and compared with the spectral energy distribution (SED) of the source. A quantitative preliminary comparison between the convolution and the intrinsic SED was performed by obtaining the sums of squared residuals for the dataset S1 - S10. We conclude that S10 (sum of squared residuals = 55:3), among the 10 sets studied, is the most promising set of parameters for the search of ALPs found in this preliminary study.