  Singularity or negativity of Glauber P-function is a widespread notion of
nonclassicality, with important implications in quantum optics and with the
character of an irreducible resource. Here we explore how P-nonclassicality may
be generated by conditional Gaussian measurements on bipartite Gaussian states.
This nonclassical steering may occur in a weak form, which does not imply
entanglement, and in a strong form that implies EPR-steerability and thus
entanglement. We show that field quadratures are the best measurements to
remotely generate nonclassicality, and exploit this result to derive necessary
and sufficient conditions for weak and strong nonclassical steering. For
two-mode squeezed thermal states (TMST), weak and strong nonclassical steering
coincide, and merge with the notion of EPR steering. This also provides a new
operational interpretation for P-function nonclassicality as the distinctive
feature that allows one-party entanglement verification on TMSTs.
