Nanotubular structures from a new family of misfit compounds LnS–TaS2 with (Ln = La, Ce, Nd, Ho, Er) and LaSe–TaSe2 (some of them not known hitherto) are reported. Stress relaxation originating from the lattice mismatch between the alternating LnS(Se) and TaS2(Se) layers, combined with seaming of the dangling bonds in the rim, leads to the formation of a variety of nanotubular structures. Their structures are studied via scanning electron microscopy (SEM), high-resolution transmission electron microscopy (HRTEM), scanning transmission electron microscopy (STEM) and selected area electron diffraction (SAED). Tubules exhibiting a single folding vector for the LnS(Se) as well as TaS2(Se) layers were often found. The small values of the c-axis periodicities are indicative of a strong interaction between the two constituent layers which was also supported by Raman spectroscopy and theoretical calculations.