With any (not necessarily proper) edge k -colouring γ : E ( G ) ⟶ { 1 , … , k } of a graph G , one can associate a vertex colouring σ γ given by σ γ ( v ) = ∑ e ∋ v γ ( e ) . A neighbour-sum-distinguishing edge k -colouring is an edge colouring whose associated vertex colouring is proper. The neighbour-sum-distinguishing index of a graph G is then the smallest k for which G admits a neighbour-sum-distinguishing edge k -colouring. These notions naturally extend to total colourings of graphs that assign colours to both vertices and edges. We study in this paper equitable neighbour-sum-distinguishing edge colourings and total colourings, that is colourings γ for which the number of elements in any two colour classes of γ differ by at most one. We determine the equitable neighbour-sum-distinguishing index of complete graphs, complete bipartite graphs and forests, and the equitable neighbour-sum-distinguishing total chromatic number of complete graphs and bipartite graphs.