Phase composition, microstructure and mechanical properties of six complex concentrated alloys, NbTiZr, NbTiZrV, NbTiZrVMo, NbTiZrVTa, NbTiZrVCr, and NbTiZrVAl0.24, are reported. The alloy density was in the range from 6.34 g/cm3 to 8.43 g/cm3. After homogenization annealing at 1400 °C or 1200 °C, only the ternary NbTiZr alloy had a single-phase BCC crystal structure. NbTiZrV and NbTiZrVTa produced predominantly single-phase BCC structure with clusters of fine V-rich precipitates inside NbTiZrV grains and fine, Zr-rich grain boundary precipitates in NbTiZrVTa. The other three alloys contained BCC and Laves phases, and NbTiZrVMo also contained a second BCC phase. After compression deformation at 1000 °C, noticeable changes in the phase composition were found in NbTiZrV, NbTiZrVTa and NbTiZrVAl0.24, while the phase composition of other alloys retained unchanged. NbTiZr, NbTiZrV and NbTiZrVTa showed good ductility and noticeable work hardening rate at room temperature, while the ductility of other alloys rapidly decreased with increasing the amount of Laves phase. The RT yield stress varied from 975 MPa for NbTiZ to 1510 MPa for NbTiZrVMo. At 1000 °C, all the alloys showed excellent compression ductility; however only NbTiZrVCr and NbTiZrVMo were stronger than NbTiZr. The results indicate that increasing the composition complexity of refractory near-equiatomic alloys by increasing the number of the alloying elements does not necessary result in a simpler phase structure and/or better mechanical properties. The type of the alloying elements seems to be more important than their number. Additions of V, Al or Ta decrease while additions of Cr or Mo increase the 1000 °C strength of NbTiZr.