@arhayes​ If two lines meet, do you want the nearest point to be matched to the end of one of those line and the start of the next, or i there some other criteria for point near to the start/end points?

 Also, are the points already relatively close to the line ends?

NeighborFinder is probably what you are looking for, but you might need to pre- or post-processing depending on the actual configuration of your lines & points

@Mark Stoakes​ The lines are roadway segments where maintenance may need to be done. The lines are being collected via iPhone GPS by people driving the roads. The points are roadway mile markers. I want to figure out the closest mile marker point to the start and the closest mile marker point to the end of each line, so that a maintenance crew could quickly get a sense for the basic location of each line. The points have mile marker number as an attribute and the lines have empty fields for nearest begin mile marker and nearest end mile marker. If two lines meet, then I would still want the nearest mile marker to the end of the one joining line and the nearest mile marker to the beginning of the other joining line with no additional criteria. I hope this clarifies my requirements. I am relatively new to FME, but I am already finding it to be very valuable. Thanks!

@Mark Stoakes​ I'm pretty sure I figured it out. I used Snippers to get the begin (0) vertex and the end (-1) vertex of the line segments. Then I did a NeighborFinder to get the nearest mile marker for each of these vertices. And, finally, I did a PointOnLineOverlayer to get the mile marker attributes back to the original line segments.