The quantum electrodynamical theory of the two-photon transitions in hydrogenlike ions is presented. The emission probability for 2s_1/2 → 2γ(E1) + 1s_1/2 transitions is calculated and compared to the results of the previous calculations. The emission probabilities 2p _1/2 → γ(E1) + γ(E2) + 1s_1/2 and 2p _1/2 → γ(E1) + γ(M1) + 1s_1/2 are also calculated for the nuclear charge Z values 1 ≤ Z ≤ 100. This is the first calculation of the two latter probabilities. The results are given in two different gauges.