Every Saturday of the year, hundreds of couples converge on a shady park in Mexico City to embrace one another in the slow-moving, genteel dance known as the danzon.

Many of the men appear transported from the 1930s and 1940s — in zoot suits with loose-fitting jackets and high-waist tapered pants. Fedoras, graced with a lone feather, top off the retro look.

The women balance on high heels, waving fans to shoo away the heat.

Danzon lives on in corners of Mexico even though it has virtually died out in Cuba, where it evolved in the 19th century from dances and rhythms originating in Europe and Africa centuries earlier.

It is a precise, elegant dance, with the men leading in a three-step movement, dipping and swirling their partners in delicate but restrained style.

“It is a dance in which the partners touch each other in a discreet way,” said Jose Luis Ceron Mireles, a sociologist and expert on danzon (pronounced dahn-SONE). “They don’t look at each other directly. They glance at each other out of the corners of their eyes. That’s where the sensuality lies.”

To this day in public parks in Veracruz, Merida and Mexico City, as well as ballrooms in other cities, fans of the dance turn out by the hundreds while bands known as danzoneras, replete with marimbas, trumpets, drums and percussive instruments made from gourds and known as guiros, coax the music forth.

“See that guy with the hat with the feather in it? They are called pachucos. They dress like they are from the 1940s,” said Vicente Carranza Navarro as he took a break in Mexico City’s Balderas Avenue Park.

Pachuco is old-school Mexican slang for a style of dress developed in northern Mexico and in El Paso, Texas, more than six decades ago. A basic staple is the fedora with the lone feather.

“I have been doing danzon for 45 years,” said Carranza, 63, who wore a blue guayabera, the loose-fitting square-tailed shirt commonly worn in the Caribbean and along Mexico’s Gulf Coast.

The park was filled with people in their 60s and 70s — or older — but a smattering of young people, and even children, mixed in.

“My mom would come here and bring me along, so I started to learn,” said Carla Bocanegra, a 23-year-old whose partner wore an elegant white striped suit and a panama hat. “I come all Saturdays, every last one.”

Danzon developed in Cuba in the mid-1800s with roots in the English line dance known as contradance and the French square dance-like quadrille, two styles that arrived in Cuba with British invaders and French colonists fleeing the Haitian Revolution. The dance forms blended with African rhythms to make a fusion of African and European movement.

With its far-flung rhythms merged into a quintessentially creole form, the danzon allowed people of all races and social strata to intermingle.

Itinerant Cuban theater and music companies arriving in the Mexican port of Veracruz and the Yucatan city of Merida brought danzon with them.

“They’d play in the parks and on the wharves,” Ceron said. “People danced in the open air.”

As the decades passed, other dance forms evolved in Cuba, like the mambo, cha-cha-cha and salsa. Danzon took root and grew in Mexico.

“The triumph of danzon has come outside its country of origin. It’s only in Mexico where the danzon carries on,” Ceron said.