History
Neutron stars were predicted in the 1930s
as a theoretical idea. However,
they were not taken very seriously until the discovery of radio pulsars
in the 1960s pointed to rapidly rotating neutron stars as their most likely explanation.
Here are three documents online at the University of Colorado
that trace the evolution of the idea of neutron stars:
The existence of neutron stars is now considered to be certain by essentially all astronomers.