There are some indications of changes of relationships between solar activity indices during the last two solar cycles. Therefore we analyze behavior of six solar activity indices, F10.7, F30, Mg II, He II, sunspot number R and the solar Lyman-α flux Fα in two consecutive periods, 1976-1995 and 1996-2014. We observe some changes in relationships between individual solar indices from the first to the second period. It has also impact on the ionosphere. We found that the relationship between the main ionospheric parameter foF2 and solar activity proxies in the first and the second period was essentially the same for F30 and Mg II, it changed significantly for F10.7 and R and to some extent also for He II and Fα, the slope of linear dependence being steeper in the second period. Origin of these changes is hypothesized to lie probably in behavior of solar activity indices.