At the beginning of the new 24th solar cycle several geomagnetic storms were occurred. One of the most essential storms took place on May 2-3, 2010 and another one, the first geomagnetic storm with Dst index lower then -90 nT after extended solar minimum, was observed on May 29, 2010. The first storm has well pronounced positive phase before noon of 2 May, the second storm started before midnight. The ionosphere response on these events was analyzed by using the ionospheric sounding data. The three ionosondes which formed a triangle in the mid-latitudes of the central European region were selected for the given analysis. There are the “Parus” ionosonde at the observatory of the West Department of IZMIRAN (Kaliningrad, Russia) and two digisondes located in Pruhonice (Czech Republic) and Juliusruh (Germany). Also at Kaliningrad observatory variations of geomagnetic field were registered. The digisonde data were provided by the DIAS network. The ionograms derived from all ionosondes were scaled manually in order to exclude errors related with autoscaling. For comparative analysis were calculated median values for non-disturbed days of May 2010. For detailed analysis of height ionosphere structure modification we combined ionosonde derived data with the GPS COSMIC radio occultation electron density profiles. For analysis are used occultations located inside triangle formed by ionosondes. The peak electron density (foF2) variations and shape of the electron density profiles were analyzed. The differences of ionosphere responses to May 2010 geomagnetic storms were studied. The time and quantitative characteristics of the ionosphere modifications during May 2010 geomagnetic storms were revealed.