Morphological associative memories (MAMs) belong to the class of morphological neural networks. The recording scheme used in the original MAM models is similar to the correlation recording recipe. Recording is achieved by means of a maximum (MXY model) or minimum (WXY model) of outer products. Notable features of autoassociative morphological memories (AMMs) include optimal absolute storage capacity and one-step convergence. Heteroassociative morphological memories (HMMs) do not have these properties and are not very well understood. The fixed points of AMMs can be characterized exactly in terms of the original patterns. Unfortunately, AMM fixed points include a large number of spurious memories. In this paper, we combine the MXX model and variations of the kernel method to produce new autoassociative and heteroassociative memories. We also introduce a dual kernel method. A new, dual model is given by a combination of the WXX model and a variation of the dual kernel method. The new MAM models exhibit better error correction capabilities than MXX and WXX and a reduced number of spurious memories which can be easily described in terms of the fundamental memories.16625-32