Possible manifestations of accreting magnetars are discussed. It is shown that the four ultra-luminous X-ray pulsars can be understood in the accreting low magnetic field magnetar scenario. The NGC300 ULX1 pulsar may have a higher dipole magnetic field than other sources. General constraint on their mass accretion rate confirmed their super-Eddington nature. Lower limits on their beaming factor are obtained. They do not seem to have strong beaming. The duty cycle of the ULX burst state can also be constrained by their timing observations. ULX pulsars may be in accretion equilibrium in the long run. During the outburst, they will spin up, and run from the previous equilibrium state to the new equilibrium state. It is proposed that the slowest puslation X-ray pulsar AX J1910.7+0917 may be an accreting magnetar with a low mass accretion rate. ULX pulsars, slow pulsation X-ray pulsars may all be accreting magnetars with different accretion rates. Seven possible signatures of an accreting magnetar are summarized.

Assuming wind-fed accretion magnetars in long-period X-ray pulsars, we calculated the rotational evolution of neutron stars. Our calculations considered the effects of magnetic field decay in magnetars. The results show that wind-fed accretion magnetars can evolve to long-period X-ray pulsars with a spin period much longer than 1000 s. The spin-down trend observed in 4U 2206+54-like sources is expected when young X-ray binary systems are on the way to their equilibrium period. Detailed calculations showed that the spin-down may be affected by accretion with outflows or accretion while spinning down. Due to magnetic field decay in magnetars, wind-fed accretion magnetars will have a decreasing equilibrium period for a constant mass accretion rate. For 2S 0114+65, the spin-up rate due to magnetic field decay is one order of magnitude smaller than observations. The spin-up rate of 2S 0114+65 may be attributed to the formation of a transient disc during wind accretion. The slowest X-ray pulsar AX J1910.7+0917 would be a link source between 4U 2206+54 and 2S 0114+65.

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