************************************************************************* 61043 Recently it has become evident that there is a small subgroup of X-ray pulsars, with pulse periods close to 6 sec. These pulsers are characterized by the very steep soft spectrum, relatively low lominosity and secular spin-down trend. 4U0142+61, 1E2259+586, and 1E1048.1-5937 are the typical example of this subclass and they were once observed with ASCA in 1993 to 1994. Currently the most likely interpretation is that these pulsars are single neutron stars accreting matter from a disk, the recent remnants of the common-envelope evolution of a high-mass X-ray binary. We propose that the observations of these pulsar with ASCA again in five years' interval is crucially effective to examine the currently proposed hypotesis for the origin of this cluss pulsars. *************************************************************************