A remarkable distinction between boron and carbon hydrides lies in their extremely different bonding patterns and chemical reactivity, resulting in diverse areas of application. Particularly, carbon, characterized by classical two‐center – two‐electron bonds, gives rise to organic chemistry. In contrast, boron forms numerous exotic and non‐intuitive compounds collectively called non‐classical structures. It is reasonable to anticipate that other elements of Group 13 exhibit their own unusual bonding patterns; however, our knowledge of the hydride chemistry for other elements in Group 13 is much more limited, especially for the heaviest stable element, thallium. In this work, we performed a conformational analysis of Tl2Hx and Tl3Hy (x=0–6, y=0–5) series via Coalescence Kick global minimum search algorithm, DFT, and ab initio quantum chemistry methods; we investigated the bonding pattern using the AdNDP algorithm, thermodynamic stability, and stability toward electron detachment. All found global minimum structures are classified as non‐classical structures featuring at least one multi‐center bond.