  We show that subpresentations of aspherical prounipotent presentations over
fields of zero characteristics and subpresentations of aspherical
pro-$p$-presentations are aspherical, an application to subpresentations of
aspherical discrete presentations is also included. Following Bousfield-Kan,
Quillen and Sullivan the results are regarded as affirmative answers to
rational and $p$-adic analogs of J.H.C. Whitehead's conjecture.
