AbstractA subset S of V is called a total dominating set if every vertex in V is adjacent to some vertex in S. The total domination number γt(G) of G is the minimum cardinality taken over all total dominating sets of G. A dominating set is called a connected dominating set if the induced subgraph 〈S〉 is connected. The connected domination number γc(G) of G is the minimum cardinality taken over all minimal connected dominating sets of G. In this work, we characterize trees and unicyclic graphs with equal total domination and connected domination numbers.