On 15 May 2005, a huge interplanetary coronal mass ejection (ICME) was observed near Earth. It triggered one of the most intense geomagnetic storms of solar cycle 23 (Dstpeak = −263 nT). This structure has been associated with the two-ribbon flare, filament eruption, and coronal mass ejection originating in active region 10759 (NOAA number). We analyze here the sequence of events, from solar wind measurements (at 1 AU) and back to the Sun, to understand the origin and evolution of this geoeffective ICME. From a detailed observational study of in situ magnetic field observations and plasma parameters in the interplanetary (IP) medium and the use of appropriate models we propose an alternative interpretation of the IP observations, different to those discussed in previous studies. In our view, the IP structure is formed by two extremely close consecutive magnetic clouds (MCs) that preserve their identity during their propagation through the interplanetary medium. Consequently, we identify two solar events in Hα and EUV which occurred in the source region of the MCs. The timing between solar and IP events, as well as the orientation of the MC axes and their associated solar arcades are in good agreement. Additionally, interplanetary radio type II observations allow the tracking of the multiple structures through inner heliosphere and pin down the interaction region to be located midway between the Sun and the Earth. The chain of observations from the photosphere to interplanetary space is in agreement with this scenario. Our analysis allows the detection of the solar sources of the transients and explains the extremely fast changes of the solar wind due to the transport of two attached (though nonmerging) MCs which affect the magnetosphere.