Process for producing a web of an elastic nonwoven composite material, comprising the following steps: supplying and conveying a first nonwoven ply (4, 4a) in a longitudinal direction; supplying a multitude of elastic filaments in the longitudinal direction; supplying a second nonwoven ply (10, 10a); combining the second nonwoven ply (10, 10a) with the first nonwoven ply (4, 4a) in such a way that the elastic filaments are arranged in a sandwich-like manner between the first nonwoven ply (4, 4a) and second nonwoven ply (10, 10a) to form a layer arrangement, passing the layer arrangement through a press nip of a calender roll pair for bonding of the layer arrangement to form a material composite by means of a binding pattern comprising bonded regions and unbonded regions, where the binding pattern produces first melt bonds directly between the first and second nonwoven plies (4, 4a, 10, 10a), and where the unbonded regions form a clear space between the first and second nonwoven plies, overstretching at least regions of the first nonwoven ply (4, 4a) and the second nonwoven ply in the longitudinal direction by passing the material composite through the nip of a pair of profiled, intermeshing stretching rolls, which extends the material composite in the longitudinal direction, where the elastic filaments are arranged in the nonwoven composite material such that they are oriented essentially in the longitudinal direction, such that they have at most 10 points of intersection with one another per cm 2, characterized in that prior to the bonding of the nonwoven plies (4, 4a, 10, 10a) particulate materials are applied to the first or second nonwoven ply in such a way that the particulate materials after the bonding of the nonwoven plies (4, 4a, 10, 10a) are arranged in a sandwich-like manner between the nonwoven plies (4, 4a, 10, 10a), where at least 80% by weight of the particulate materials has a particle size of 45-1200 μm and where, after the bonding of the nonwoven plies (4, 4a, 10, 10a), a multitude of the particulate materials has been introduced within the clear space. supplying and conveying a first nonwoven ply (4, 4a) in a longitudinal direction; supplying a multitude of elastic filaments in the longitudinal direction; supplying a second nonwoven ply (10, 10a); combining the second nonwoven ply (10, 10a) with the first nonwoven ply (4, 4a) in such a way that the elastic filaments are arranged in a sandwich-like manner between the first nonwoven ply (4, 4a) and second nonwoven ply (10, 10a) to form a layer arrangement, passing the layer arrangement through a press nip of a calender roll pair for bonding of the layer arrangement to form a material composite by means of a binding pattern comprising bonded regions and unbonded regions, where the binding pattern produces first melt bonds directly between the first and second nonwoven plies (4, 4a, 10, 10a), and where the unbonded regions form a clear space between the first and second nonwoven plies, overstretching at least regions of the first nonwoven ply (4, 4a) and the second nonwoven ply in the longitudinal direction by passing the material composite through the nip of a pair of profiled, intermeshing stretching rolls, which extends the material composite in the longitudinal direction, where the elastic filaments are arranged in the nonwoven composite material such that they are oriented essentially in the longitudinal direction, such that they have at most 10 points of intersection with one another per cm 2, characterized in that prior to the bonding of the nonwoven plies (4, 4a, 10, 10a) particulate materials are applied to the first or second nonwoven ply in such a way that the particulate materials after the bonding of the nonwoven plies (4, 4a, 10, 10a) are arranged in a sandwich-like manner between the nonwoven plies (4, 4a, 10, 10a), where at least 80% by weight of the particulate materials has a particle size of 45-1200 μm and where, after the bonding of the nonwoven plies (4, 4a, 10, 10a), a multitude of the particulate materials has been introduced within the clear space.