The CeCr2Al20-type aluminides RETi2Al20 (RE = Eu, Gd, Tb, Dy and Yb), space group
F
d
3
‾
m
$Fd\overline{3}m$
, show the formation of solid solutions RETi2Al20−x
Ga
x
with gallium in the ranges 0 ≤ x ≤ 10. Polycrystalline samples were prepared from the elements in alumina crucibles or directly via arc-melting followed by annealing in order to increase crystallinity. The structures of six single crystals were refined from single crystal X-ray diffractometer data for determining the precise occupancy parameters of the aluminum and gallium atoms. The solubility limit of gallium was found at around x ≈ 10. The RETi2Al20−x
Ga
x
structures show a MgCu2-related substructure of the rare earth and titanium atoms. The Al/Ga atoms then form Frank-Kasper type polyhedra around the RE and Ti atoms, i. e., RE@(Al/Ga)16 and Ti@(Al/Ga12). These are the basic building units of the RETi2Al20−x
Ga
x
structures. Temperature-dependent magnetic susceptibility studies show Pauli paramagnetic behavior for the YbTi2Al10Ga10 sample, i. e., a stable divalent ytterbium ground state.