Two-ring resonance-assisted hydrogen bond (RAHB) systems can be obtained by merging two cis enol ring of malondialdehyde with different orientations. In the present work, a comparative theoretical study of all of the possible two-ring RAHB systems, 2,3-dihydroxy-2-butene-4-dial (DBD), 1,5-dihydroxy-1,4-diene-3-pentanone (DDP) and 2-dihydroxy-methylene-propanediol (DMP), was carried out. Also, the influence of the co-existence of two RAHB rings on the molecular structures, intramolecular hydrogen bond (IMHB) and the p-electron delocalization (p-ED) was investigated. In this regard, ab initio calculations on the various equilibrium conformations of DBD, DDP and DMP at MP2/6-311??G(d,p) level of theory have been performed and the IMHB strength of model compounds by different descriptors such as geometrical, topological, molecular orbital, spectroscopic and energetic parameters was evaluated. Then, the p-ED of DBD, DDP and DMP was estimated by using a variety of indicators, such as geometrical factor of Gilli (k), the harmonic oscillator model of aromaticity, the nucleus-independent chemical shift, the para delocalization index, the average two-center index, the aromatic fluctuation index. Finally, based on the computational results, it was found that the strength of IMHB and significance of p-ED in two-ring RAHB systems are strongly related to the relative flow of p-electrons in two rings. In other words, the parallel flows of p-electrons in DMP and DDP increase the IMHB strength and p-ED, while opposite flow of p-electrons in DBD decreases the IMHB strength and p-ED.