This paper describes the use of two-beam line-confocal detection geometry for measuring the total mobility of individual molecules undergoing continuous-flow CE separation. High-sensitivity single-molecule confocal detection is usually performed with a diffraction limited focal spot (similar to 500nm in diameter), which necessitates the use of nanometer-sized channels to ensure all molecules flow through the detection volume. To allow for the use of larger channels that are a few micrometers in width, we employed cylindrical optics to define a rectangular illumination area that is diffraction-limited (similar to 500 nm) in width, but a few micrometers in length to match the width of the microchannel. We present detailed studies that compare the performance of this line-confocal detection geometry with the more widely used point-confocal geometry. Overall, we found line-confocal detection to provide the highest combination of signal-to-background ratio and spatial detection efficiency when used with micrometer-sized channels. For example, in a 2 Pin wide channel we achieved a 94% overall detection efficiency for single Alexa488 dye molecules when a 2 mu m x 0.5 mu m illumination area was used, but only 34% detection efficiency with a 0.5 mu m diameter detection spot. To carry out continuous-flow CE, we used two-beam fluorescent cross-correlation spectroscopy where the transit time of each molecule is determined by cross-correlating the fluorescence registered by two spatially offset line-confocal detectors. We successfully separated single molecules of FITC, FITC-tagged glutamate, and FITC-tagged glycine.