There is a great interest in photonic substances with permittivity approaching zero, which are called the epsilon-nearzero (ENZ) materials. They have a potential for multiple applications in telecom industry. The newest ENZ materials based on transparent conductive oxides (TCOs) and transparent conductive nitrides (TCNs) still have limited spectral bands of the ENZ effect. We show with simulations based on the Effective Medium Theory that the limitation can be defeated by using nanocomposite films made of several TCOs/TCNs with the ENZ effect observed in different regions of optical spectrum that stand apart from each other. We proposed to make such composites with the concurrent multibeam multi-target pulsed laser deposition (CMBMT-PLD). The composite films of aluminum and gallium doped zinc oxide (AZO-GZO) at different proportions were made by concurrent PLD of AZO and GZO targets with two 532-nm laser beams from a frequency doubled Q-switched Nd:YAG laser in a 10<sup>-5</sup>-Torr vacuum. The deposition time varied from 10 to 50 min. The high-resolution scanning electron microscopy revealed that the films deposited on glass substrates were composed of nano-grains of the constituents with a size in the range 10-300 nm. Energy dispersive X-ray spectroscopy showed the presence of all the major constituents in the films. Optical absorption and reflection spectroscopy of the films in the visible and near-infrared regions demonstrated that they had a minimum of reflectance corresponding to the ENZ effect in a broad band (~ 200 nm) around 1200 nm in the agreement with theoretical predictions.