  We succeed to generalize spun knots of classical 1-knots to the virtual
1-knot case by using the `spinning construction'. That, is, we prove the
following: Let $Q$ be a spun knot of a virtual 1-knot $K$ by our method. The
embedding type $Q$ in $S^4$ depends only on $K$. Furthermore we prove the
following: The submanifolds, $Q$ and the embedded torus made from $K,$ defined
by Satoh's method, in $S^4$ are isotopic.
  We succeed to generalize the above construction to the virtual 2-knot case.
Note that Satoh's method says nothing about the virtual 2-knot case. Rourke's
interpretation of Satoh's method is that one puts `fiber-circles' on each point
of each virtual 1-knot diagram. If there is no virtual branch point in a
virtual 2-knot diagram, our way gives such fiber-circles to each point of the
virtual 2-knot diagram. We prove the following: If a virtual 2-knot diagram
$\alpha$ has a virtual branch point, $\alpha$ cannot be covered by such
fiber-circles.
  We obtain a new equivalence relation, the $\mathcal E$-equivalence relation
of the set of virtual 2-knot diagrams, by using our spinning construction. We
prove that there are virtual 2-knot diagrams that are virtually nonequivalent
but are $\mathcal E$-equivalent.
  Although Rourke claimed that two virtual 1-knot diagrams $\alpha$ and $\beta$
are fiberwise equivalent if and only if $\alpha$ and $\beta$ are welded
equivalent, we state that this claim is wrong. We prove that two virtual 1-knot
diagrams $\alpha$ and $\beta$ are fiberwise equivalent if and only if $\alpha$
and $\beta$ are rotational welded equivalent.
