Recently, Weinhold et al. put forward one new concept of (sigma) over cap -type long-bonding and applied it to the comprehension of halogen noble-gas hydrides HNgY (Ng = noble gas; Y = halogen) bonding. The present study extends this new concept into HNgX (X = CN, NC) pseudohalogen molecules. At the B3LYP and CCSD(T) levels of theory, we perform natural bond orbital (NBO) and natural resonance theory (NRT) studies on the HNgX molecules and compare them with the previous results for HNgY molecules. The NBO/NRT results clearly reveal that each of the HNgX, but not the HHeCN, HNeCN, and HNeNC molecules, is composed of three leading resonance structures: two omega-bonding structures H-Ng(+) :X-, H:Ne--(+)-X and one long-bonded structure H<^>X. This result indicates that the conventional long-bonding exists in these pseudohalogen molecules, like the long-bonding in HNgY molecules. Unexpectedly, we identify a new type of longer long-bonded structure HAC in HNeNC molecule at the B3LYP level, which disappears at the CCSD level. This misleading prediction at the B3LYP level can be traced back to the singlet diradical character, which induces a low-quality geometry. Therefore, the geometry reoptimization of the noble-gas hydrides is indispensable using CASSCF-based methods, if the noble-gas hydrides fail the "Stable" test because of diradical-type instability.