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Relative intensity noise (RIN) spectra of weakly index guided vertical-cavity surface-emitting lasers (VCSELs) in a multitransverse-mode regime are analyzed by using a model that takes into account all the transverse modes supported by the waveguide. Several resonance peaks are obtained in the noise spectra that correspond to the relaxation oscillation frequencies of the transverse modes. It is shown that for low spatially overlapping transverse modes, low RIN operation can be maintained. However, the excitation of transverse modes with a significant spatial overlap leads to a clear enhancement of the RIN at low frequencies.