D-branes on some one- and two-parameter Calabi-Yau hypersurfaces

D-branes on one-parameter Calabi-Yau spaces and two-parameter K3-fibered Calabi-Yau manifolds are analyzed from both the Gepner model point of view and the geometric perspective. We compute part of the spectrum of the boundary states and comment on the appearance of the D0-brane as well as on nonsupersymmetric large volume configurations becoming supersymmetric at the Gepner point.