Is this kind of art created in Illustrator?

[garnetius]

I’m thinking multiple layers of gradient meshes.

I was unable to recreate the technique in Photoshop with any kind of desirable result, but an old tutorial on Illustrator seems promising.

I'm talking about the front sides, of course. The verso are obvious.

Please advice.

[Myra Ferguson]

Although the business cards appear to be based on a watercolor-style effect that you could make in Photoshop with brushes, you could try reproducing the effect in Illustrator with gradient meshes (like the tutorial you posted) or a freeform gradient. You would probably need to also apply a raster effect, though, by going to Effect > Effect Gallery... or using a plugin like Texturino from Astute Graphics.