We characterize bounded sets in ultradistributions spaces
D
L
t
′
(
M
p
)
,
t
∈
[
1
,
∞
]
,
S
′
{
M
p
}
\mathcal {D}_{{L^t}}^{’({M_p})},\,t \in [1,\infty ],\,S{’^{\{ {M_p}\} }}
, and
S
′
(
M
p
)
S{’^{({M_p})}}
and bounded sets and convergent sequences in
D
′
(
M
p
)
\mathcal {D}{’^{({M_p})}}
and
D
′
{
M
p
}
\mathcal {D}{’^{\{ {M_p}\} }}
via the convolution by corresponding test functions. The structural theorems for
D
L
t
′
{
M
p
}
\mathcal {D}_{{L^t}}^{’\{ {M_p}\} }
and
D
~
L
t
′
{
M
p
}
,
t
∈
[
1
,
∞
]
\widetilde D_{{L^t}}^{’\{ {M_p}\} },\;t \in [1,\infty ]
, are also given.