The closely related crystal structures of the compounds La6Ni2Si3 (La12Ni4Si6, n = 2) and La5Ni2Si3 (La20Ni8Si12, n = 3) as well as those of the new compounds La15Ni7Si10 (La30Ni14Si20, n = 4) and La21Ni11Si15 (La42Ni22Si30, n = 5) were determined from single-crystal X-ray diffractometer data. In these hexagonal silicides (space group P6(3)/m) almost all atoms are situated on mirror planes, which extend perpendicular to the short c axes. The only exceptions are nickel atoms located on the 6(3) axes, which show some disorder resulting in the exact compositions La6Ni1.54(2)Si-3 [a = 1224.3(1) pm, c = 438.3(1) pm, Z = 2, Ce6Ni2Si3 type structure], La5Ni1.75(1)Si-3 [a = 1624.4(3) pm, c = 434.2(2) pm, Z = 4, Ce5Ni2Si3 type], La15Ni6.62(2)Si-10 [a = 2021.2(3) pm, c = 435.1(1) pm, Z = 2, Pr15Ni7Si10 type], and La21Ni10.49(3)Si-15 [a = 2427.7(3) pm, c = 435.2(1) pm, Z = 2, a new structure type]. All of these structures have building elements; which resemble the AlB2 type structure. In these the lanthanum atoms correspond to the aluminum atoms of AlB2, while the nickel and silicon atoms occupy the boron positions in an ordered manner. Other series of ternary hexagonal lanthanoid and actinoid transition metal silicides and phosphides, e.g., the series with the general formula Rn(n-1)Ni(n+1(n+2))Pn(n+1+1) (R = Th, U), are briefly reviewed, and the systematics in the space groups and the diffraction patterns of these compounds are pointed out.