A novel feature of Layered Manufacturing, an emerging manufacturing technology, is that it enables fabrication of heterogeneous objects (multi-material and functionally graded interiors). In our earlier work, we developed new modeling schemes (called heterogeneous solid models) for representing these heterogeneous objects by capturing both geometry and material information. One of the crucial steps for fabricating these heterogeneous objects in LM is adaptive slicing, a fundamental process planning task. In this paper, we describe how the heterogeneous solid models can be adaptively sliced to aid in the LM fabrication of heterogeneous objects.