| Award | Season | |
|---|---|---|
| Golden Globe Award for Best Television Series - Drama (1989) | - | winner |
| Golden Globe Award for Best Television Series - Drama (1990) | - | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1989) | Season 2 | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1990) | Season 3 | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1991) | Season 4 | shortlisted |