  Using BRST-BV approach, massless and massive continuous-spin fields
propagating in the flat space are studied. For such fields, BRST-BV gauge
invariant Lagrangian is obtained. The Lagrangian and gauge transformations are
constructed out of traceless gauge fields and traceless gauge transformation
parameters. Interrelation between the BRST-BV Lagrangian and the Lagrangian for
the continuous-spin fields in metric-like approach is demonstrated. Considering
the BRST-BV Lagrangian in the Siegel gauge, we get gauge-fixed Lagrangian which
is invariant under global BRST and antiBRST transformations.
