As Colin Blunstone, lead singer of The Zombies, sees it, it’s a very strange story.

In 1967, The Zombies recorded a song and an album that would only belatedly achieve classic status. The Zombies, much less popular in their native England than The Rolling Stones, The Kinks, The Who and, of course, The Beatles, disbanded that same year. But The Zombies were ahead of their time. The public, critics and radio ignored The Zombies’ now classic album, “Odessey and Oracle,” featuring the haunting, late-blooming hit “Time of the Season,” upon its original release in 1968.

Four years before, The Zombies’ 1964 hit, “She’s Not There,” became the first song by a post-Beatles British band to go to No. 1 in the U.S. Another hit, “Tell Her No,” followed in 1965. And then the hits stopped.

The Zombies, the current lineup of which features original members Blunstone and Rod Argent, will play their first New Orleans show Thursday at the House of Blues. A debut 51 years in the making, the show is being presented by The Ponderosa Stomp Foundation in association with House of Blues.

“It’s absolutely true,” Blunstone said from his home on the outskirts of London. “The original incarnation of the band came to the states three times. We came close to New Orleans, but we never, ever got there. I don’t know why that is, but we’re really looking forward to (performing in New Orleans). It’s a city so rich in history and, in particular, musical history.”

Blunstone and Argent reunited in 1999 for an intended six gigs only. Their partnership continued, however, and, by popular demand, after years of reluctance, they again began billing themselves The Zombies.

But back in 1967, The Zombies felt unappreciated, especially in Britain. Nevertheless, that year they wrote and recorded their masterpiece, “Odessey and Oracle.” The album ranks at 100 on Rolling Stone’s Top 500 rock albums of all time. In 2013, The Zombies were nominated for induction into the Rock and Roll Hall of Fame.

The Zombies recorded “Odessey and Oracle” at Abbey Road Studios, a few months after The Beatles crafted “Sgt. Pepper’s Lonely Hearts Club Band” there. CBS Records gave the band a small, 1,000-pound budget. With no time to linger in the expensive facility, Blunstone, Argent, Chris White, Paul Atkinson and Hugh Grundy rehearsed the songs thoroughly before entering Abbey Road.

“When we got to the studio,” Blunstone said, “it was the quality of the sounds that we were looking for and, of course, the actual performance. We knew exactly what we were going to do and we recorded very quickly.”

When the “Odessey and Oracle” sessions were over, Blunstone thought he and his fellow Zombies had done the best work they could do. “And I loved all the songs,” he said.

Released in April 1968, “Odessey and Oracle” entered the world largely unnoticed.

“Nothing really happened with the album a’ tall,” Blunstone recalled. “I’m sitting in England thinking, ‘Well, this is the best we can possibly do and we can’t get any airplay. We can’t chart the album. We can’t even get it released in America. And so it seemed like it was the right time for us to move on. We just decided to look for new projects.”

But “Odessey and Oracle” had a fan in America. Al Kooper — a session musician, former member of Blood, Sweat & Tears and a newly hired producer at Columbia Records — secured the album’s stateside release. As it did in Britain, it flopped, but one song from the album would, in a roundabout way, rise to the top.

“There’s an old story that was told to me as a true story, that there was a DJ — I never was told his name — in Boise, Idaho, who would not stop playing ‘Time of the Season.’ Through his perseverance, it gradually got onto playlists of neighboring stations and then onto bigger stations. It wasn’t promoted or marketed, as far as I’m aware. Of course, there was no promotion from the band because the band didn’t exist.”

In early 1969, “Time of the Season” reached No. 3 on the Billboard singles chart and No. 1 at Cashbox. The ex-Zombies, Blunstone recalled, were “utterly and absolutely shocked.” About a decade later, a second surprise came when “Odessey and Oracle” finally attracted popularity and acclaim.

“It picked up lots of wonderful reviews and it started to sell,” Blunstone said. “It’s gone on selling. It sells more now than it did when it was released.”

Argent and Blunstone stayed in music after the Zombies’ first run, but their post-Zombies projects usually weren’t noticed in the U.S.

“This is a stamina business,” the singer said. “It’s not a sprint; it’s a marathon. And you’ve got to be resilient. You have to be a little tough, but at the same time, to be an artist, you have to be sensitive as well. Everybody gets these knock-backs all the time. Pick yourself up, brush yourself down and start all over again. The more times you get knocked down, the harder it is to get up. But you have to do it.”