Production of carcass structures and/or production of crown structures includes: positioning a first continuous elongated element so that its end stretch is aligned with a cutting position; positioning a second continuous elongated element so that its end stretch is in side by side relationship with the end stretch of the first continuous elongated element; forming first strip-like elements from the first continuous elongated element; depositing the first strip-like elements on at least one forming drum; translating the end stretches of the first and second continuous elongated element in a transverse direction relative to their longitudinal extension to align the end stretch of the second continuous elongated element to said cutting position; forming second strip-like elements from the second continuous elongated element; and depositing the second strip-like elements on said at least one forming drum.