This paper presents an approach to programming and running scientific applications on grid and cloud infrastructures based on two principles: the first one is to follow a component-based programming model, the second is to apply a flexible technology which allows for virtualization of the underlying infrastructure. The solutions described in this paper include high-level composition and deployment consisting of a scripting-based environment and a manager system based on an architecture description language (ADL), a dynamically managed pool of component containers, and interoperability with other component models such as Grid Component Model (GCM). We demonstrate how the proposed methodology can be implemented by combining the unique features of the Common Component Architecture (CCA) model together with the H2O resource sharing platform, resulting in the MOCCA component framework. Applications and tests include data mining using the Weka library, Monte Carlo simulation of the formation of clusters of gold atoms, as well as a set of synthetic benchmarks. The conclusion is that the component approach to scientific applications can be successfully applied to both grid and cloud infrastructures.