The epidermis of the adult Drosophila abdomen is formed by a chain of anterior (A) and posterior (P) compartments, each segment comprising one A and one P compartment. In the accompanying paper (Struhl et al., 1997), we provide evidence that Hedgehog protein (Hh), being secreted from P compartment cells, organises the pattern and polarity of A compartment cells. Here we test whether Hh acts directly or by a signal relay mechanism. We use mutations in Protein Kinase A (PKA) or smoothened (smo) to activate or to block Hh signal transduction in clones of A compartment cells. For cell type, a scalar property, both manipulations cause strictly autonomous transformations: the cells affected are exactly those and only those that are mutant. Hence, we infer that Hh acts directly on A compartment cells to specify the various types of cuticular structures that they differentiate. By contrast, these same manipulations cause non-autonomous effects on cell polarity, a vectorial property. Consequently, we surmise that Hh influences cell polarity indirectly, possibly by inducing other signalling factors. Finally, we present evidence that Hh does not polarise abdominal cells by utilising either Decapentaplegic (Dpp) or Wingless (Wg), the two morphogens through which Hh acts during limb development. We conclude that, in the abdomen, cell type and cell polarity reflect distinct outputs of Hh signalling and propose that these outputs are controlled by separable gradient and signal relay mechanisms.