The process of making and breaking reversible bonds between associating gro
ups (stickers) controls the dynamics of associating polymers. We develop a
theory of "sticky reptation" to model the dynamics of entangled solutions o
f associating polymers with many stickers per chain. At a high degree of as
sociation, there are very few unassociated stickers. It is therefore very d
ifficult for a sticker to find a new partner to associate with after breaki
ng the bond with an old one. Typically a sticker returns to its old partner
following an unsuccessful search for a new one, prolonging the effective l
ifetime of reversible bonds. In the sticky reptation model, the search for
a new partner is restricted to a part of the tube confining the entangled c
hain. Another important effect is the increase of the fraction of the inter
chain associations at the expense of the intrachain ones with increasing po
lymer concentration. The sticky reptation model predicts a very strong conc
entration dependence of viscosity in good agreement with experiments.