Results are reported of an investigation on the velocity of a single straight magnetic domain wall in a Ga:YIG film as a function of the drive field and of a static magnetic field applied perpendicular to the wall in the plane of the film. At all drive fields a substantial increase of the wall velocity was observed when the in-plane field was applied. At an in-plane field of about 400 Oe and at a rather low drive field (2.4 Oe above the coercive field) a maximum value in wall velocity of 270 ms
-1was observed. At higher drive fields the wall velocity decreased to a constant value of 110 ms
-1, independent of the drive field. This behavior can be explained by extending Slonczewski\´s theory of domain wall motion to the present case. From the observed wall mobility parameter we have calculated the reduced Landau-Lifshitz damping constant

(

Oe
2s). This value is near to the value obtained by Spencer and LeCraw from linewidth measurements in FMR on Ga:YIG spheres (

Oe
2s).