Sarevok's Tome

If you're already in a dungeon when instructed to venture into Undercity, you move to the next room of that dungeon. If you are already in the last room, you will complete that dungeon and start Undercity. This is true whether you're already in Undercity or any other dungeon.

In a Two-Headed Giant game, if both players on a team deal combat damage to the player that has the initiative at the same time, the player with the initiative will choose the order of the triggered abilities. Then, as those abilities resolve, one team member takes the initiative (and ventures into Undercity) and then the other team member does the same. The last player to take the initiative keeps it until the initiative changes again.

If you aren't in a dungeon when instructed to venture into Undercity, you will put Undercity into the command zone and move your venture marker to Secret Entrance (the first room).