In a boiler (6) having a shell (8) enclosing a space (11) and an inlet (12) for letting water into the shell space (11), the shell space (11) has two separate sections (16, 21), wherein a first section (16) is located such as to receive a supply of fresh water to the boiler (6), and wherein a second section (21) is located such as to receive water from the first section (16) when overflow of the first section (16) takes place under the influence of a continuous supply of fresh water. A steam generating process takes place in the second section (21). Due to the fact that the second section (21) is only indirectly filled with water, it is possible to have an undisturbed process. In particular, the water may be heated in the first section (16) before reaching the second section (21). The first section (16) may comprise an inner space of a container (15) which is arranged inside the shell (8), for example.