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We present theoretical studies of syntectic and monotectic solidification scenarios. Steady-state solidification along the liquid-liquid interface in a syntectic system is considered by means of a boundary-integral technique developed previously. We study the case of small asymmetry of the pattern and extract from the results the scaling relations in terms of the undercooling and the asymmetry parameter. We also investigate monotectic solidification using the phase-field method. We present two kinds of two-phase fingers, with the solid phase being either the exterior phase or the interior phase, and the pattern corresponding to the growth along the solid-liquid interface. We finally analyze the asymptotic shape of these new morphologies far behind their tip.