Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 10.54216/PAMDA https://www.americaspg.com/journals/show/3864 2022 2022 Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan Takaaki Takaaki An algorithm is a finite, well-defined computational procedure that transforms inputs into outputs through a structured sequence of steps, guaranteeing termination and correctness. A multialgorithm comprises multiple algorithms augmented with a selection mechanism that dynamically chooses the most appropriate procedure based on input characteristics or contextual conditions. While these concepts have deep roots in computer science and beyond, this paper introduces two novel generalizations: the Hyperalgorithm and the Superhyper- algorithm. By leveraging the mathematical frameworks of hyperstructures and superhyperstructures, respectively, we extend the classical notion of computation to higher-order operations on sets and iterated powersets. We present formal definitions, illustrative examples, and a preliminary analysis of their computational properties, laying the groundwork for a unified theory of higher-order algorithms. 2024 2024 36 49 10.54216/PAMDA.040104 https://www.americaspg.com/articleinfo/34/show/3864