I have two drives that I would like to backup.  One drive (the smaller) changes frequently and I would like to do incremental backups daily with a new full backup every week.  The second drive (much larger - takes 4 hours to do a full backup) changes infrequently and I would like to back it up weekly (incremental) with a full backup only every month.  I would like both backups to occur in the early morning when other activities are minimal.  As both backups are to the same network drive, I would really not like them to conflict by running at the same time.  Is there a way to set one backup to begin immediately after the other finishes?

Don 

We don't have a way to schedule tasks such that one kicks off immediately after another, however, you can generally gauge the time that a backup will take and then set the scheduled times so that if you have more than one backup job they do not occur at the same time.  In your case you will have two backup jobs - one for each volume - each job having a unique schedule.

 What will happen if the second job's start time occurs while the first job is running?

They'll both run without error.  However, they'll both run slower as they'll be competing for system resources (disk I/O bandwidth and cpu cycles).