What were the indefinite validity visas that used to be issued by the US before VWP was created?

I can't improve on Giorgio's excellent answer above, but while searching out some other paperwork I came across my old passports dating from the 1980s, one of which contains my Burroughs visa from that time, stamped in my blue British passport.

I got one (when I was child). I went in US for first time (like my family) for a full booked touristic tour. As far I know, we didn't asked anything special, I think it was the standard tourist visa for our country. Note: I was a children so no personal financial record, and US could not forecast what kind of job I would get as adult.

I used that visa twice, last use it was just few days after the "converted 10 years validity", but it was still OK. Just the Immigration officer cancelled it with a huge X, and he told us that it was converted to 10 years some time ago.

As far I know, it was cancelled not because of Machine Readable Visas, but because of introduction of Visa Waiver Program (VWP), so removing the need of a visa in such "trusted" countries. So now I doesn't need a visa (so in principle I still have a "visa of indefinite validity"). Just that in my last travel with such visa, because I had the visa, I should not complete the VWP form, now I need to do it (as ESTA form).

I have an "indefinite Class BII visa" in my 1972 passport. I was a student at the time. The application form was extremely lengthy and detailed. I had to be interviewed at the US embassy in London where they asked my three questions (also on the form): 1. Was I or had I ever been a member of the communist party. 2. How long did I intend to stay. 3. Did I jave enough funds to cover my stay. The visa (tourist) allowed me to stay up to three months. That was it. My 1972 passport was returned with a clipped corner and I was instructed to take it and present it along with my new passport as the old one had a valid "indefinate" visa. I have not travelled to the US since 1972, and many of my work colleagues were telling my that they were completing "visa" request firms on the plane journey over to the US. Sounded a little risky to me as what would happen if the visa were to be refused? Presumably an immediate return flight home! Anyhow, I understand things have changed again visa application wise due to the elevated security checking nowadays......Cheers, Jon