The measurement or constraint of the masses of neutron stars and their binary companions tests theories of neutron star structure and of pulsar formation and evolution . We have measured the rate of the general relativistic advance of the longitude of periastron for the pulsar PSR B1802 - 07 : \dot { \omega } = 0 \hbox { $ . ^ { \circ } $ } 060 \pm 0 \hbox { $ . ^ { \circ } $ } 009 \mbox { % yr } ^ { -1 } , which implies a total system mass , pulsar plus companion star , of M = 1.7 \pm 0.4 M _ { \odot } . We also present a much improved measurement of the rate of periastron advance for PSR B2303+46 : \dot { \omega } = 0 \hbox { $ . ^ { \circ } $ } 0099 \pm 0 \hbox { $ . ^ { \circ } $ } 0002 \mbox% { yr } ^ { -1 } , implying M = 2.53 \pm 0.08 M _ { \odot } for this system . We discuss the available constraints on distribution of mass between the pulsars and their companions , and we compare the pulsar masses with other determinations of neutron star masses .