A continuous sequence of compounds having composition NbxTa1-xTe4; 0 ≤ x ≤ 1 have been studied by electron diffraction and microscopy. Previous studies have shown that the end members of the series, TaTε4 and NbTε4 possess a quasi-one-dimensional character and exhibit charge density wave (CDW) distortions. In these compounds, the subcell structure is tetragonal with axes (a × a × c) and consists of the metal atoms (Nb or Ta) centered within an extended antiprismatic cage of Te atoms. At room temperature, TaTε4 has a commensurate modulation structure with a 2a × 2a × 3c unit cell. In NbTε4, an incommensurate modulation with × ∼ 16c axes is observed. Preliminary studies of the mixed compounds NbxTα1-xTε4 showed a discontinuous jump of the modulation wave vector commensurate to incommensurate when the Nb dopant concentration x, exceeded x ≃ 0.3, In this paper, the nature of the compositional dependence of is studied in greater detail and evidence is presented for a stepwise variation of . This constitutes the first direct evidence for a Devil's staircase in CDW materials.