For a connected graph G of order at least two, a total monophonic set of a graph G is a monophonic set S such that the subgraph G[S] induced by S has no isolated vertices. The minimum cardinality of a total monophonic set of G is the total monophonic number of G and is denoted by mt(G). We determine bounds for it and characterize graphs which realize the lower bound. Also, some general properties satisfied by this concept are studied. It is shown that for positive integers a, b such that 3 ≤ a ≤ b with b ≤ 2a, there exists a connected graph G such that m(G) = a and mt(G) = b. Further, if p, a, b are positive integers such that 4 ≤ a ≤ b ≤ p, then there exists a connected graph G of order p with mt(G) = a and mc(G) = b, where mc(G) is the connected monophonic number of G.