<p>The first and second Gourava indices of a hypergraph are defined in terms of the sum and product of the degrees of the vertices contained in each hyperedge. These indices act as structural descriptors that capture the degree distribution and interaction patterns within hypergraphs, thereby extending the concept of Gourava indices originally proposed for simple graphs. In this paper, we establish bounds on the first and second Gourava indices for general, <i>k</i>-uniform, and bipartite hypergraphs. Furthermore, bounds are derived in terms of the size, order, and extremum degrees of the hypergraph. In addition, various hypergraph operations are examined, and the extremal values of the Gourava indices are determined in relation to other well-known degree-based topological indices. The results obtained may be useful for descriptor-based modelling, network analysis, and structural studies of industrial and infrastructure systems.</p>