Hi Barb,
I'm assuming you're in Word 2003 and working in
the Drawing Canvas?
Once the connectors are hooked to a shape you can
get the blue 'connection points' if you 'grab' the
connected end of one line and pull it away from the shape
it is connected to and continue to hold down the left
mouse button while you 'hover' the 'free' connector
end near an autoshape.
=====
I am trying to connect two autoshapes and see the blue indicator only once
when trying to connect the shapes. Does anyone have any idea why I can't
select the shape to connect? >>
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Let us know if this helped you,
Bob Buckland ?

MS Office System Products MVP
*Courtesy is not expensive and can pay big dividends*
Office 2003 Editions explained
http://www.microsoft.com/uk/office/editions.mspx