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High sensitivity H I observations of the nearby spiral galaxy NGC 2403obtained with the VLA are presented and discussed. The properties of theextended, differentially rotating H I layer with its H I holes, spiralstructure and outer warp are described. In addition, these new data reveal thepresence of a faint, extended and kinematically anomalous component. This showsup in the H I line profiles as extended wings of emission towards the systemicvelocity. In the central regions these wings are very broad (up to 150 km/s)and indicate large deviations from circular motion. We have separated theanomalous gas component from the cold disk and have obtained for it a separatevelocity field and a separate rotation curve. The mass of the anomalouscomponent is 1/10 of the total H I mass. The rotation velocity of the anomalousgas is 25-50 km/s lower than that of the disk. Its velocity field hasnon-orthogonal major and minor axes that we interpret as due to an overallinflow motion of 10-20 km/s towards the centre of the galaxy. The pictureemerging from these observations is that of a cold H I disk surrounded by athick and clumpy H I layer characterized by slower rotation and inflow motiontowards the center. The origin of this anomalous gas layer is unclear. It islikely, however, that it is related to the high rate of star formation in thedisk of NGC 2403 and that its kinematics is the result of a galactic fountaintype of mechanism. We suggest that these anomalous H I complexes may beanalogous to a part of the High Velocity Clouds of our Galaxy.Comment: 35 pages, 13 Postscript figures. Accepted for pubblication by A

Deep H [CSC]i[/CSC] Survey of the Spiral Galaxy NGC 2403