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Published online by Cambridge University Press: 21 February 2013
We consider the evolution of the very young neutron stars (NS) with moderate and low magnetic field values around 1E8 G to know how large is the share of the these objects among the those attributed as the millisecond pulsars (MSP). To exclude the contamination of accreted NS and young NS with moderate magnetic fields we study the observational evidences of the accretion on NS in the binary systems and different methods of age determinations. It was concluded that only central compact objects are appropriate candidates for NSs with small initial magnetic fields.