Laser remelting experiments have been performed with austenitic stainless steels to evaluate the effects of composition (Cr/Ni-equivalent between 1.52 and 1.61) and solidification velocity (V_s=1 to 30 mm/s) on the phase selection between primary δ-ferrite and primary γ-austenite. Experimental results were compared with previous work. The Cr/Ni-equivalent is useful to predict the transition from δ to γ by comparison with microstructural transitions in the Fe-Cr-Ni ternary system. The δ to γ transitions can be modeled by the dendrite growth theory for multicomponent systems. The calculated results show the potential of this approach for the analysis of microstructure formation.