Like fossils, multiple stellar and gaseous components with a misaligned or even opposite angular momentum with respect to that of their host conserve memory of processes driving galaxy formation and evolution. In disk galaxies, apart few cases like polar rings, they usually lurk to morphological inspection, they are serendipitously discovered by measuring detailed kinematics and generally interpreted as the end result of one or more second events. This is the case of a variety of kinematically-decoupled components, like the counterrotating gas observed in several S0's, the counterrotating stellar or gaseous disks found in a number of early-type spirals, and the orthogonally-rotating stellar cores we recently discovered in the bulges of two Sa spirals, namely NGC 4698 and NGC 4672. In this contribution we present the results of a survey aimed to measure the stellar and ionized-gas kinematics in a sample of nearby S0/a's and Sa's, which have been selected to be morphologically similar to the few spiral galaxies hosting counterrotating stellar and/or gaseous disks. In spite of their undisturbed appearance, all the sample galaxies host a kinematically decoupled gas component since they are characterized by a sharp gas velocity gradient along their minor axes. In some cases the nuclear gas is even rotating perpendicularly to the galaxy disk. In the past numerical experiments predicted that observable consequences of second events in disk galaxies (e.g. bulge growing, disk heating) result in a change of the host morphology toward earlier spiral types. Now we attempt to investigate the possible link between morphology and second events (unveiled by kinematical decouplings) in early-type spirals.