The Electronic-Topological (ETM) and Neural Network methods were applied to the study of the "structure-acetylcholinesterase (AChE) inhibitor activity" relationships for a series of physostigmine and N-benzylpiperidine derivatives. Molecular fragments specific for active compounds and breaks of activity were calculated for human AChE by applying the ETM and Neural Network methods. Requirements necessary for a compound to be active were formulated; they are the result of detailed analysis of all compounds under study. A comparative study of the activity features found for human AChE was performed.