We have searched for thermal dust emission from circumstellar disks ar
ound five neutron stars using the Owens Valley millimeter array at 99
GHz and the James Clerk Maxwell Telescope at 380 GHz. Two of the neutr
on stars (PSR 0950+08 and 1133+16) are nearby isolated pulsars with ch
aracteristic ages 10(6) to 10(7) yr. The remaining three (PSR 1257+12,
1534+12, and 1937+21) are old millisecond pulsars with ages in the ra
nge 10(8) to 10(9) yr. None of the pulsars was detected above the nois
e, giving 2 a limits on the mass of disk material of approximately 10(
-2) M. if their disks are similar to those around pre-main-sequence st
ars. We discuss mechanisms for clearing dust grains from circumpulsar
disks. We show that dust particles orbiting a neutron star lose angula
r momentum due to the ram pressure of the interstellar medium, which i
s approximately 10(4) times stronger for pulsars than for normal stars
because of their high space velocity. For a pulsar moving at 100 km s
-1 through an ambient medium with number density n approximately 1 cm-
3, dust grains 0.1 mum in size spiral into the star in approximately 1
0(6) years. This mechanism is more effective at clearing grains than t
he Poynting-Robertson effect and may limit the detectability of disks
around old neutron stars.