  A Smarandache quasigroup(loop) is shown to be universal if all its
f,g-principal isotopes are Smarandache f,g-principal isotopes. Also, weak
Smarandache loops of Bol-Moufang type such as Smarandache: left(right) Bol,
Moufang and extra loops are shown to be universal if all their f,g-principal
isotopes are Smarandache f,g-principal isotopes. Conversely, it is shown that
if these weak Smarandache loops of Bol-Moufang type are universal, then some
autotopisms are true in the weak Smarandache sub-loops of the weak Smarandache
loops of Bol-Moufang type relative to some Smarandache elements. Futhermore, a
Smarandache left(right) inverse property loop in which all its f,g-principal
isotopes are Smarandache f,g-principal isotopes is shown to be universal if and
only if it is a Smarandache left(right) Bol loop in which all its f,g-principal
isotopes are Smarandache f,g-principal isotopes. Also, it is established that a
Smarandache inverse property loop in which all its f,g-principal isotopes are
Smarandache f,g-principal isotopes is universal if and only if it is a
Smarandache Moufang loop in which all its f,g-principal isotopes are
Smarandache f,g-principal isotopes. Hence, some of the autotopisms earlier
mentioned are found to be true in the Smarandache sub-loops of universal
Smarandache: left(right) inverse property loops and inverse property loops.
