In this review the basic properties of nonrotating and slowly rotating protoneutron stars in the relativistic mean-field approach are discussed .
The equation of state is the main input to the structure equations .
The TM1 parameter set extended to the case of finite temperature is used to obtain the mass-radius relation for protoneutron stars .
The occurrence of unstable areas in the mass-radius relation are presented .
This allows for the existence of distinctively different evolutionary of tracks of the protoneutron stars .
The low density protoneutron star configurations are estimated .
The obtained stable configurations for the fixed lepton number Y _ { L } = 0.4 are compared with ones obtained for the fixed proton fraction Y _ { P } = 0.1776 .