The main purpose of this paper is to define a point of departure for a systematic study of internal categorical structures in a category with a given \(2\)-cell structure (or sesquicategory), and also to investigate how these categorical structures are changed when the given \(2\)-cell structure over the base category varies. More concretely, in this work we can find an extension of the notion of pseudocategory internal to a \(2\)-category to the more general setting of a pseudocategory internal to a sesquicategory. The article is organized as follows. In section 2, the author recalls the notions of internal (pre)category, internal (pre)functor and internal (natural) transformation and also introduce some useful notation. In section 3, he considers an arbitrary fixed category, \(\mathbf{C}\), and define a 2-cell structure over it, as to make it a sesquicategory. In this section we can find a characterization of that structure as a family of sets, together with maps and actions, satisfying some conditions that generalizes the description of \(2\)-Ab-categories as families of abelian groups, together with group homomorphisms and laws of composition, which may be found in two previous papers of the same author: [in: Galois theory, Hopf algebras, and semiabelian categories. Papers from the workshop on categorical structures for descent and Galois theory, Hopf algebras, and semiabelian categories, Toronto, ON, Canada, September 23–28, 2002. . 387–410 (2004; Zbl 1067.18005); Appl. Categ. Struct. 18, No. 3, 309–342 (2010; Zbl 1206.18005)]. Section 4 is devoted to introduce some necessary ingredients, i.e., the notions of cartesian square with respect to a specified \(2\)-cell structure, and the notions of natural and invertible \(2\)-cell structures. Section 5 is dedicated to examples and section 6 is the one where we can find the notion of pseudocategory internal to a sesquicategory. The main example presented by the author is the study of pseudocategories in the sesquicategory of abelian chain complexes with homotopies as 2-cells. Finally, it is interesting to point out that, using the analogy between geometric vectors in the plane and \(2\)-cells between morphisms, in this paper the author introduce a different notation for the vertical composition of \(2\)-cells: instead the usual dot \(\cdot \)’ or \(\bullet\)’, he used \(+\)’.