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Regular high-precision timing of the binary pulsars J0613−0200, J1012+5307, J1022+1001, J1640+2224, J1643−1224, J1713+0747, J2145−0750 and the pulsar B1937+21 has been conducted at the Kalyazin (Russia) radio telescope RT-64 at 0.6 GHz over more than 6 years. Several of the pulsars monitored have been found to be good probes for gravitational wave background (GWB) tests, while others, having a shorter orbital period, can be used for establishing a dynamical binary pulsar timescale. Upper limits for the GWB energy density were estimated.