Accretion is a dominant factor in the early evolution of stars. The first time an accretion regime settles in is when a dusty opaque core forms. The mass of adiabatically contracting core inside the isothermally collapsing envelope depends only on the optical properties of dust. Spherically symmetric models of dusty cores were constructed using the Henyey technique with accretion boundary conditions (Menshchikov 1986). It appears that all protostars with normal chemical composition should pass through the stage of a quasistatic dusty core. The evolution of dusty cores is similar to that of “normal” young stars with accretion. One could distinguish convective, radiative and central core contraction phases. The life-time tc of the core depends on the core mass Mc and the accretion rate Ṁ (for Mc = 0.01 M⊙ and Ṁ = 1.6x10−6, 1.6x10−5 M⊙/year tc = 1.2x104, 3x103 yrs consequently). After dust exhaustion in the core it collapses and a central ionized quasistatic region grows in several tens of years. A flash of infrared radiation at the moment is not excluded.