A machine for treating or conveying containers, comprising a guide extending along a feed direction for feeding the containers and a plurality of carriages for supporting the containers slidably mounted on a same guide consecutively to each other; said guide and each carriage together defining respective linear motors. Each support carriage comprises at least a part of respective gripping means and, in particular, two gripping means respectively mounted on different and consecutive carriages along the same guide. The carriages are movable towards or away from each other so as to regulate the reciprocal distance along the feed direction for feeding the containers and define a picking area of the gripping means between them as a function of the type of container to be picked or released.