We introduce a new concept of Fano-like resonances for the extinction cross-section at light scattering by small (relative to the light wavelength) particles. The resonances occur beyond the applicability of the Rayleigh approximation, when the interference of different electromagnetic modes excited in the particle with the same multipole moment is crucial, while the partition of the incident wave bypassing the particle is unimportant. We present two examples of these fundamentally new Fano-like resonances: at the light scattering by a particle with large dielectric permittivity and by a particle with spatial dispersion. In both cases the extinction cross-section as a function of the incident light frequency exhibits a sequence of the Fano-like resonances, while each individual resonance is described by the conventional Fano profile.