Kernel density estimates, as commonly applied, generally have no exact model-based interpretation since they violate conditions that define coherent joint distributions. The issue of marginalization consistency is considered here. It is shown that most commonly used kernel functions violate this condition. It is also shown that marginalization consistency holds only for classes of kernel estimates based on Laplacian, or double-exponential kernels whose window width parameters are appropriately structured. The practical relevance and implications of this result are discussed. © 1991 Biometrika Trust.