In all known examples of metal-ligand (M-L) δ and φ bonds, the metal orbitals are aligned to the ligand orbitals in a "head-to-head" or "side-to-head" fashion. Here, we report two fundamentally new types of M-L δ and φ interactions; "head-to-side" δ and "side-to-side" φ back-bonding, found in complexes of metallacyclopropenes and metallacyclocumulenes of actinides (Pa-Pu) that makes them distinct from their corresponding Group 4 analogues. In addition to the known Th and U complexes, our calculations include complexes of Pa, Np, and Pu. In contrast with conventional An-C bond decreasing, due to the actinide contraction, the An-C distance increases from Pa to Pu. We demonstrate that the direct L-An σ and π donations combined with the An-L δ or φ back-donations are crucial in explaining this non-classical trend of the An-L bond lengths in both series, underscoring the significance of these δ/φ back-donation interactions, and their importance for complexes of Pa and U in particular.