We discuss the Hankel determinants H2(n)=anan+2-an+12 for typically real functions, that is, analytic functions which satisfy the condition Im ⁡z Im⁡f(z)≥0 in the unit disk Δ. Main results are concerned with H2(2) and H2(3). The sharp upper and lower bounds are given. In general case, for n≥4, the results are not sharp. Moreover, we present some remarks connected with typically real odd functions.