Two superposed layers of transparent cylindrical lenslet gratings create classical moiré fringes, when illuminated from behind. We rely on this observation to conceive special devices made of superposed lenslet gratings that produce animated moirés when they are tilted against the light. One-dimensional moirés can show a message moving back and forth along a given direction or radially expanding towards the exterior of a disk. These 1D moirés are conceived by fabricating two layers of micro-lenses on both sides of a transparent substrate. The top layer is a rectilinear grating of cylindrical lenslets and the bottom layer is an arrangement of smaller lenslets of different sizes and orientations that create a high contrast. Moirés created by superpositions of lenslets are visually striking and can be challenging to fabricate. Therefore they have a high potential for art, decoration, and document security.