The unique solvability of the two-phase Stefan problem with a small parameter ε∈ ∈[0; ε ₀] at the time derivative in the heat equations is proved. The solution is obtained on a certain time interval [0; t ₀] independent of ε. The solution of the Stefan problem is compared with the solution to the Hele-Shaw problem corresponding to the case ε∈=∈0. The solutions of both problems are not assumed to coincide at the initial moment of time. Bibliography: 18 titles.