Depending on the specialty and the type of eConsult, you have anywhere between 1-5 hours to accept your eConsult. After you accept a case, you have a fresh 3 hours to respond before it will be re-routed to a peer.
Cases assigned during evenings (after 8 pm EST) and weekends will have an extended acceptance period. After you accept the case, you will still have 3 hours to respond.
A new case will appear in your "Taskbox" window, and the case status will say "New request." Before you accept or decline a case, the expiration time is available on the consult: