  This is a sequel to our work in tropical Hodge theory. Our aim here is to
prove a tropical analogue of the Clemens-Schmid exact sequence in asymptotic
Hodge theory. As an application of this result, we prove the tropical Hodge
conjecture for smooth projective tropical varieties which are rationally
triangulable. This provides a partial answer to a question of Kontsevich who
suggested the validity of the tropical Hodge conjecture could be used as a test
for the validity of the Hodge conjecture.
