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A significant part of barred disc galaxies exhibits boxy/peanut-shapedstructures (B/PS bulges) at high inclinations. Another structure alsoassociated with the bar is a barlens, often observed in galaxies in a positionclose to face-on. At this viewing angle, special kinematic tests are requiredto detect a 3D extension of the bars in the vertical direction (B/PS bulges).We use four pure $N$-body models of galaxies with B/PS bulges, which havedifferent bar morphology from bars with barlenses to the so-called face-onpeanut bars. We analyse the kinematics of our models to establish how thestructural features of B/PS bulges manifest themselves in the kinematics forgalaxies at intermediate inclinations and whether these features are related tothe barlenses. We apply the dissection of the bar into different orbital groupsto determine which of them are responsible for the features of the LOSVD(line-of-sight velocity distribution), i.e., for the deep minima of the $h_4$parameter along the major axis of the bar. As a result, we claim that for ourmodels at the face-on position, the kinematic signatures of a `peanut' indeedtrack the vertical density distribution features. We conclude that orbitsresponsible for such kinematic signatures differ from model to model. We payspecial attention to the barlens model. We show that orbits assembled intobarlens are not responsible for the kinematic signatures of B/PS bulges. Theresults presented in this work are applicable to the interpretation of IFUobservations of real galaxies.

B/PS bulges and barlenses from a kinematic viewpoint. I