Apparatus for inspecting transparent, cylindrical containers containing transparent or semi-transparent viscous or gel products, in particular for medical applications, comprising: - a support and/or gripping device for a cylindrical container, suitable for supporting it and provided with means for making it rotate about a vertical rotation axis (Y-Y), coincident with a cylindrical axisymmetry axis (X-X) of said cylindrical container, - a video camera directed so as to frame and capture images of a window of a side wall of the cylindrical container, - said side wall having a thickness equal to the difference between an outer radius (Re), i.e. a radius of an outer surface of the side wall, with respect to the cylindrical axisymmetry axis (X-X), and an inner radius (Ri), i.e. a radius of an inner surface of the side wall, - a lighting device, placed opposite the video camera with respect to the cylindrical container, so as to back-light said cylindrical container, - a control unit operatively connected to the support and/or gripping device and to the video camera, and programmed to: - control the rotation of the cylindrical container by means of the support and/or gripping device at constant angular speed around the vertical rotation axis (Y-Y), - control the activation of the video camera so as to acquire a plurality of 'n' images of said window, for a predetermined number 'n' of regular angular intervals (Δθ), - identify points (Pi) of said images which can be catalogued as impurities, characterized in that the control unit is further programmed to - measure a median displacement (ΔSmed) of each of said points (Pi) during said regular angular intervals Δθ and compare it to a discriminating value equal to the product of the internal radius (Ri) of the cylindrical container and said regular angular intervals (Δθ), and - classify the impurity identified by the point (Pi) as external to the container if said median displacement (ΔSmed) of the point (Pi) is greater than said discriminating value and vice versa. - a support and/or gripping device for a cylindrical container, suitable for supporting it and provided with means for making it rotate about a vertical rotation axis (Y-Y), coincident with a cylindrical axisymmetry axis (X-X) of said cylindrical container, - a video camera directed so as to frame and capture images of a window of a side wall of the cylindrical container, - said side wall having a thickness equal to the difference between an outer radius (Re), i.e. a radius of an outer surface of the side wall, with respect to the cylindrical axisymmetry axis (X-X), and an inner radius (Ri), i.e. a radius of an inner surface of the side wall, - a lighting device, placed opposite the video camera with respect to the cylindrical container, so as to back-light said cylindrical container, - a control unit operatively connected to the support and/or gripping device and to the video camera, and programmed to: - control the rotation of the cylindrical container by means of the support and/or gripping device at constant angular speed around the vertical rotation axis (Y-Y), - control the activation of the video camera so as to acquire a plurality of 'n' images of said window, for a predetermined number 'n' of regular angular intervals (Δθ), - identify points (Pi) of said images which can be catalogued as impurities, characterized in that the control unit is further programmed to - measure a median displacement (ΔSmed) of each of said points (Pi) during said regular angular intervals Δθ and compare it to a discriminating value equal to the product of the internal radius (Ri) of the cylindrical container and said regular angular intervals (Δθ), and - classify the impurity identified by the point (Pi) as external to the container if said median displacement (ΔSmed) of the point (Pi) is greater than said discriminating value and vice versa. - control the rotation of the cylindrical container by means of the support and/or gripping device at constant angular speed around the vertical rotation axis (Y-Y), - control the activation of the video camera so as to acquire a plurality of 'n' images of said window, for a predetermined number 'n' of regular angular intervals (Δθ), - identify points (Pi) of said images which can be catalogued as impurities, characterized in that the control unit is further programmed to - measure a median displacement (ΔSmed) of each of said points (Pi) during said regular angular intervals Δθ and compare it to a discriminating value equal to the product of the internal radius (Ri) of the cylindrical container and said regular angular intervals (Δθ), and - classify the impurity identified by the point (Pi) as external to the container if said median displacement (ΔSmed) of the point (Pi) is greater than said discriminating value and vice versa.