Interesting one. My first thought was The Shadows, but that turns out to be wrong as there were pre-Marvin/Welch members who are no longer with us. My next thought was 10cc whose founder members were active in various guises in the mid-60s but the band didn't officially form until around 1972. They are all still "above grass" (as Rutherford put it) though.
I'm drawing a blank after that so far.
Great question. I think all of the original line up of the Hollies from 1963/4 are alive. I’ve had a quick check add will double check later.
But they are not really a rock band so may not count
Great question. I think all of the original line up of the Hollies from 1963/4 are alive. I’ve had a quick check add will double check later.
But they are not really a rock band so may not count
I would count them as a "rock band," but according to what I see in Wikipedia, their original bassist died in 2019.
I would count them as a "rock band," but according to what I see in Wikipedia, their original bassist died in 2019.
you are quite right, back to the drawing board! Thanks
The zombies?
The zombies?
Paul Atkinson (guitarist) R.I.P.
In Italy were famous The Rokes. 
In Italy were famous The Rokes.
Excellent shout rkive. They meet the criteria. If we are only thinking in terms of Rock Bands formed in England (According to Wiki The Rokes were formed in Italy by English ex-pats) it may well just be Genesis. But I’m still looking and thinking.
Just to add to this, of all the members who have ever been in Genesis, only one (John Mayhew) has passed.
Just to add to this, of all the members who have ever been in Genesis, only one (John Mayhew) has passed.
Yep. It's hard to name any major band from the '60s or '70s with that good of a "survival rate."
For example, both the Doobie Brothers (founded 1970) and Traffic (founded 1967) have had 14 members of which 7 are deceased. (And in the case of Traffic, the surviving members include 3 guys who didn't join until the 1994 reunion tour. So, from the band's original 1967-74 run, only 4 out of 11 guys are still around.)
There was a similar discussion on another forum. I think it was agreed that Golden Earring (formed 1961) still has all founding members alive. But, that was a few years ago, and might not be true anymore.
Black Sabbath is close, 1968, but clearly doesn't meet the criteria of the original question.
I may as well mention Dire Straits have only lost Jack Sonni. All founding members (Knopfler brothers, Pick Withers, John Illsley) are still with us.
Supertramp
Formed around 1970 so after Genesis.....but all original members alive.....and funny enough my wife went to a Rod Stewart Tribute show last week and the drummer for the band was the original Supertramp drummer (Keith Baker)....so for sure he was still alive last week!!! 
Wishbone Ash
Looks like all original member still alive. Formed in 1969 so around the same time frame as Genesis.
Slade, 1966, albeit with band name changes, but that applies to Genesis too (FGTR not attributed to Genesis at the time) - at least 2 of them still active, Jim Lea and Don Powell, together and separately.
Stackridge? Not sure about this one, but don't recall hearing of any passing.
