We have observed several emerging flux regions (EFRs) using the Video Spectra-Spectro-Heliograph (VSSHG) at the San Fernando Observatory (SFO). The best studied region, NOAA 7968, was near disk center when it was observed on 5-8June 1996. This EFR showed no organized upflow between the leader and follower spots over the 4-day period covered by our observations. The main concentrations of magnetic flux in the region (leader and follower) showed a slow separation as flux emerged, but little or no upflow was seen. Two other EFRs were observed for part of a single day each and one region was observed for only one sequence. For all regions observed, no discrete features were seen between the leader and follower polarity sunpots that had upflowing material as the regions grew. In all cases, the downward velocities were smaller in area than the magnetic parts of the regions. At times there were several localized areas of greater-amplitude downflows near sunspots.