Self-propelled apparatus with sensors for on-condition inspection and maintenance of the underbody of trains movable on a rail track comprising: - a platform having a maximum transverse dimension, with reference to the forward direction of said rail track, smaller than the size of the gauge of the rails forming said rail track, characterized in that the self-propelled apparatus further comprises - movement organs of said platform arranged for supporting said platform on said rails and allow their sliding therealong, wherein said movement organs include: - an active group comprising at least four first rolling bodies revolving around a relative rotation axis positioned two per rail to roll on the inner profile of the shank of the rail, constrained to said platform by first support arms extending transversely from said platform and arranged to slide with respect to said platform in a direction having a predominant transverse component, at least one by side of said first rolling bodies being motorized, - a passive group comprising at least four second rolling bodies positioned two per rail to roll on the rail foot via second support arms suitable to support at one end thereof said second rolling bodies in a freely rotatable manner and rigidly constrained at their other end to said platform via connecting organs, said active group and said passive group being arranged to support said platform below the rolling surface of the rail and adapted to avoid the interference with fixing members of said rails on a plane even in the presence of trains on said rail tracks. - a platform having a maximum transverse dimension, with reference to the forward direction of said rail track, smaller than the size of the gauge of the rails forming said rail track, characterized in that the self-propelled apparatus further comprises - movement organs of said platform arranged for supporting said platform on said rails and allow their sliding therealong, wherein said movement organs include: - an active group comprising at least four first rolling bodies revolving around a relative rotation axis positioned two per rail to roll on the inner profile of the shank of the rail, constrained to said platform by first support arms extending transversely from said platform and arranged to slide with respect to said platform in a direction having a predominant transverse component, at least one by side of said first rolling bodies being motorized, - a passive group comprising at least four second rolling bodies positioned two per rail to roll on the rail foot via second support arms suitable to support at one end thereof said second rolling bodies in a freely rotatable manner and rigidly constrained at their other end to said platform via connecting organs, said active group and said passive group being arranged to support said platform below the rolling surface of the rail and adapted to avoid the interference with fixing members of said rails on a plane even in the presence of trains on said rail tracks. - an active group comprising at least four first rolling bodies revolving around a relative rotation axis positioned two per rail to roll on the inner profile of the shank of the rail, constrained to said platform by first support arms extending transversely from said platform and arranged to slide with respect to said platform in a direction having a predominant transverse component, at least one by side of said first rolling bodies being motorized, - a passive group comprising at least four second rolling bodies positioned two per rail to roll on the rail foot via second support arms suitable to support at one end thereof said second rolling bodies in a freely rotatable manner and rigidly constrained at their other end to said platform via connecting organs, said active group and said passive group being arranged to support said platform below the rolling surface of the rail and adapted to avoid the interference with fixing members of said rails on a plane even in the presence of trains on said rail tracks.