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NA61/SHINE is a multi-purpose fixed-target experiment located at the Super Proton Synchrotron at CERN. The main goals of the experiment include studies for physics of strong interactions, neutrino physics, and cosmic-rays physics. After the upgrade of the detector system, the experiment will collect data up to 1 kHz event rate. The development of new detectors, used to measure the positions of incoming beam particles in the transverse plane, is a crucial part of the upgrade. Two new kinds of beam position detectors are prepared and tested. One of them is the scintillating fiber detector with a multi-anode photomultiplier readout. It is built of two perpendicularly arranged ribbons, each consisting of two shifted layers of green-emitting scintillating fibers with a diameter of 250 μm. The second type of detector is based on single-sided silicon strip detector (Hamamatsu S13804). The paper gives an overview of both detectors’ design and readout concepts.