We know far more about the velocity and density distributions of gas in ordinary spirals than in barred spirals. There are several reasons for this : the absence of a nearby barred spiral, the circumstance that several of the best objects lie rather far south, the necessity to map in two dimensions, and the surprisingly low intensity of the emission lines, except in the nucleus and near the ends of the bar. The older literature contains several investigations of radial velocities measured along the bars of barred spirals (cf. Burbidge, Burbidge and Prendergast, 1960 a,b for NGC 7479 and NGC 3504), and it has been known for some time that rotation curves taken in different position angles through the nuclei of barred spirals are not compatible with simple circular motion. It was not until recently, however, that attempts were made to map the velocity fields of barred spirals in two dimensions. Chevalier and Furenlid (1978) studied NGC 7723, NGC 5383 has been mapped by Peterson, Rubin, Ford and Thonnard (1978) in the optical and by Sancisi, Allen and Sullivan (1979) in neutral hydrogen, and NGC 1300 has been mapped by Peterson and Huntley (1980). The most striking result of these observations is that the isovelocity contours are elongated in the direction of the bars, or, put differently, there is no straight line through the center of a barred spiral along which the radial velocity is constant. This is clear proof that significant non-circular motions are present in these galaxies. However, as it is impossible to reconstruct a non-axisymmetric velocity field from radial velocity data alone, there is no analog for barred spirals of the reduction models which are used to estimate local mass densities for ordinary spirals from observed rotation curves.