We propose an efficient inverse design approach for multifunctional optical elements based on deep diffractive neural networks (D 2 NNs). Specifically, we implement D 2 NNs for the design of two-layer diffractive devices that can selectively focus incident radiation over two well-separated spectral bands at designed distances. We investigate focusing efficiencies at two wavelengths and achieve targeted spectral lineshapes and spatial point-spread functions (PSFs) with optimal focusing efficiency. In particular, we demonstrate control of the spectral bandwidths at separate focal positions beyond the theoretical limit of single lens devices with the same aperture size. Finally, by directly training D 2 NNs using targeted PSFs below the diffraction limit, we demonstrate devices that produce superoscillatory focal spots at desired wavelengths. The proposed method is suitable for the inverse design of multi-level diffractive devices in different materials and platforms that require designed focusing and spectral responses over multiple wavelength bands simultaneously. Moreover, it is compatible with current diffractive optics and metasurface technology for ultracompact multispectral imaging and microscopy applications.