A portable electronic device, comprising an orientable case, in particular of rectangular shape, adapted to be held in hand by a user in either one of two "portrait" and "landscape" orientations, the case comprising a front face directed towards the user, a back face opposed to the front face, and a peripheral edge wall with four sides corresponding to the four sides of the rectangular shape, the device comprising means for automatically determining the "portrait" or "landscape" orientation of the case, and means for selectively switching functions of the device according to the orientation of the case, the means for automatically determining the "portrait" or "landscape" orientation of the case comprising: - a lateral touch-sensitive surface, extending over the peripheral edge wall, and first detection means, adapted to detect the contact of at least one area of the hand of the user on the lateral touch-sensitive surface and to produce as an answer hand position information corresponding to the position of the area of the hand, or to the respective positions of the areas of the hand, on the lateral touch-sensitive surface; and - discriminating means (44, 46), adapted to determine the "portrait" or "landscape" orientation of the case based on the hand position information, characterized in that: - the means for automatically determining the "portrait" or "landscape" orientation further comprise a back touch-sensitive surface, extending over the back face of the case, and second detection means (32, 36), adapted to detect the contact of at least two fingers of the user on the back touch-sensitive surface, and to produce as an answer finger position information corresponding to the respective positions of the different fingers on the back touch-sensitive surface; - the second detection means are adapted to calculate a mean distance of alignment of the positions of the different fingers on the back touch-sensitive surface; and - the discriminating means are adapted to determine the "portrait" or "landscape" orientation of the case based on combined finger position and hand position information. - a lateral touch-sensitive surface, extending over the peripheral edge wall, and first detection means, adapted to detect the contact of at least one area of the hand of the user on the lateral touch-sensitive surface and to produce as an answer hand position information corresponding to the position of the area of the hand, or to the respective positions of the areas of the hand, on the lateral touch-sensitive surface; and - discriminating means (44, 46), adapted to determine the "portrait" or "landscape" orientation of the case based on the hand position information, - the means for automatically determining the "portrait" or "landscape" orientation further comprise a back touch-sensitive surface, extending over the back face of the case, and second detection means (32, 36), adapted to detect the contact of at least two fingers of the user on the back touch-sensitive surface, and to produce as an answer finger position information corresponding to the respective positions of the different fingers on the back touch-sensitive surface; - the second detection means are adapted to calculate a mean distance of alignment of the positions of the different fingers on the back touch-sensitive surface; and - the discriminating means are adapted to determine the "portrait" or "landscape" orientation of the case based on combined finger position and hand position information.