| Award | Season | |
|---|---|---|
| Golden Globe Award for Best Television Series - Drama (1984) | - | winner |
| Golden Globe Award for Best Television Series - Drama (1985) | - | winner |
| Golden Globe Award for Best Television Series - Drama (1986) | - | shortlisted |
| Golden Globe Award for Best Television Series - Drama (1987) | - | shortlisted |
| Golden Globe Award for Best Television Series - Drama (1988) | - | shortlisted |
| Golden Globe Award for Best Television Series - Drama (1989) | - | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1985) | Season 1 | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1986) | Season 2 | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1987) | Season 3 | shortlisted |