Hi Len! NLJR drafts Rnds 14 to 35 using the web interface.
Rnds 36+ happen via a weekly email draft. Each team gets one tradeable pick per week starting a few weeks into the season with Rnd 36 and ending with the week that postseason rosters are due (approx. Rnd 55).
There is also a special 3 Round draft at the end of spring training, called the X Rounds, which allows owners to react to spring training news and injuries, and was created a few years ago in response to the fewer innings that starting pitchers are providing each year.