This work reports on electron spin resonance experiments in oriented single crystals of the hexagonal AlB2 diboride compound (P6/mmm, D16h structure) which display conduction electron spin resonance. The X-band electron spin resonance spectra showed a metallic Dysonian resonance with g-value and intensity independent of temperature. The thermal broadening of the anisotropic electron spin resonance linewidth ΔH tracks the T-dependence of the electrical resistivity below T is approximately equal to 100 K. These results confirm the observation of a conduction electron spin resonance in AlB2 and are discussed in comparison with other boride compounds. Based on our main findings for AlB2 and the calculated electronic structure of similar layered honeycomb-like structures, we conclude that any array of covalent B-B layers potentially results in a conduction electron spin resonance signal. This observation may shed new light on the nature of the non-trivial conduction electron spin resonance-like signals of complex f-electron systems such as β-YbAlB4.