The aromaticity and dynamics of a set of recently proposed neutral 5- and 6-membered heterocycles that are closed by dative (donor-acceptor) or multi-center σ bonds, and have resonance forms with a Hückel number of π-electrons, are examined. The donors and acceptors in the rings include N, O, and F, and B, Be, and Mg, respectively. The planar geometry of the rings, coupled with evidence from different measures of aromaticity, namely the NICSzz, and NICSπzz components of the conventional nucleus independent chemical shifts (NICS), and ring current strengths (RCS), indicate non-trivial degrees of aromaticity in certain cases, including the cyclic C3B2OH6 and C3BOH5 isomers, both with three bonds to the O site in the ring. The former is lower in energy by at least 17.6 kcal mol-1 relative to linear alternatives obtained from molecular dynamics simulations in this work. Some of the other systems examined are best described as non-aromatic. Ring opening, closing, and isomerization are observed in molecular dynamics simulations for some of the systems studied. In a few cases, the ring indeed persists.