The lower bridge was built in the late 1890s by the Virginia & Southwest Virginia rail road (V&SW).  That line was absorbed into the Southern Rail Road in 1916, just a year after this card was mailed.

The upper one, the Copper Creek Viaduct (a word the Marx Brothers had fun with in The Cocoanuts) was built by the C.C. & O in 1908.  The stated height now is 185′ , measuring from the river below.

You barely read the writing down the length of the viaduct, but I believe it says “crossed this just today” or something to that effect.

The post card itself appears to have been printed in Germany before WWI.