| Award | Season | |
|---|---|---|
| Golden Globe Award for Best Television Series - Drama (1983) | - | shortlisted |
| Golden Globe Award for Best Television Series - Drama (1984) | - | shortlisted |
| Golden Globe Award for Best Television Series - Drama (1985) | - | shortlisted |
| Golden Globe Award for Best Television Series - Drama (1986) | - | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1983) | Season 2 | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1984) | Season 3 | shortlisted |
| Primetime Emmy Award for Outstanding Drama Series (1985) | Season 4 | winner |
| Primetime Emmy Award for Outstanding Drama Series (1986) | Season 5 | winner |
| Primetime Emmy Award for Outstanding Drama Series (1987) | Season 6 | shortlisted |