MOTIVATION: Current spectral unmixing methods for multiplex fluorescence microscopy have a limited ability to cope with high spectral overlap as they only analyze spectral information over individual pixels. Here, we present adaptive Morphologically Constrained Spectral Unmixing (MCSU) algorithms that overcome this limitation by exploiting morphological differences between sub-cellular structures, and their local spatial context. RESULTS: The proposed method was effective at improving spectral unmixing performance by exploiting: (i) a set of dictionary-based models for object morphologies learned from the image data; and (ii) models of spatial context learned from the image data using a total variation algorithm. The method was evaluated on multi-spectral images of multiplex-labeled pancreatic ductal adenocarcinoma (PDAC) tissue samples. The former constraint ensures that neighbouring pixels correspond to morphologically similar structures, and the latter constraint ensures that neighbouring pixels have similar spectral signatures. The average Mean Squared Error (MSE) and Signal Reconstruction Error (SRE) ratio of the proposed method was 39.6% less and 8% more, respectively, compared to the best of all other algorithms that do not exploit these spatial constraints. AVAILABILITY AND IMPLEMENTATION: Open source software (MATLAB). CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.