High‐purity niobium and tantalum single crystals having orientations in the central part of the stereographic triangle and a residual resistance ratio RRR of better than 5500:1 are deformed in tension, compression, and by cyclic deformation at temperatures below ambient. The deformation behaviour is studied by observation of the slip‐line morphology, Laue X‐ray backreflection, X‐ray topography, and transmission electon microscopy (TEM). Anomalous (011) slip is observed at temperatures below about 200 K for the niobium crystals and at liquid nitrogen temperatures for the tantalum crystals, respectively. The influence of the specimen purity on the appearance of the anomalous slip is investigated by etching experiments: for example, etching in an acid solution subsequently suppresses anomalous slip in the tantalum specimens owing to the influence of hydrogen interstitials. Prestraining of the specimens has different effects on the appearance of the anomalous slip, depending on the temperature and the mode of the predeformation: anomalous slip is generally suppressed by prestraining unless the specimens are predeformed into stage I of the three‐stage work‐hardening curve at the appropriate temperatures. The TEM investigations reveal that the dislocation arrangement consists of regular networks of screw dislocations with primary and conjugate Burgers vectors, lying in the anomalous slip plane. The X‐ray topography investigations demonstrate that twist walls of alternating signs are built up during anomalous slip. The separation of two adjacent twist walls of alternating signs corresponds to the separation of the anomalous slip lines on the crystal surfaces. From the angle of twist the density of the excess dislocations in the twist walls is estimated to be about 3% of the total dislocation density.