This thesis sets out to investigate several aspects of immobilized enzymes. In particular its subject is the enzyme alkaline phosphatase (AP). One of the many aims of this thesis is to measure the activity of single immobilized AP molecules by means of total internal reflection fluorescence microscopy (TIRF). As the substrate for the enzyme, the fluorogenic molecule 3-O-methyl fluorescein phosphate (OMFP) was used, which becomes strongly fluorescent upon dephosphorylation by AP molecules. With the experimental setup it was possible to detect the activity of single enzyme molecules, which were sparsely immobilized on glass coverslips. The bright spots in the field of vision had a fluctuating intensity, which reflects a fluctuating enzymatic activity. This indicates Dynamic Disorder , an effect already observed for other enzymes. The evaluation of single enzyme data generally gives new insights into the mechanism of enzymatic action, which in bulk measurements would be obscured by averaging over a large number of enzymes. Some theoretical fundamentals of single enzyme dynamics will be reviewed and will be applied to single enzyme data.Another aim is to electrostatically control the activity of immobilized enzymes. For this purpose AP has been immobilized on the surface of a surface plasmon resonace sensor (SPR). With the SPR method it is possible to track the growth of adsorption layers on the sensor surface. The AP substrate 5-bromo-4-chloro-3-indolyl-phosphate (BCIP) with its characteristic property to precipitate after degradation by AP was used to measure the enzymatic activity indirectly. It could be shown that the application of an electric potential has a strong effect on enzymatic activity. As will be argued this is probably due to an electrostatically induced change of substrate concentration close to the surface. A third approach on AP will answer the question if a single immobilized enzyme is capable of generating a localized spot of precipitate by using BCIP as the substrate. For precipitation to take place, two product molecules need to dimerize to form indigo, which precipitates onto the support. This reaction scheme was modeled by setting up a brownian-dynamics computer simulation. The enzyme was modeled as the source of product-molecules which will, once released from the enzyme, perform random walks. If two particles collide they annihilate and a new particle is created. These new particles will diffuse unless they hit the support to be adsorbed. The insights gained from this simulation help the optimization and understanding of enzyme assisted precipitation as used for immunohistochemical applications, as well as writing with enzymes by means of Enzyme Assisted Nanolithography . Both of these applications call for the creation of nano-scaled structures