  This paper investigates Kamp-like and B\"uchi-like theorems for 1-clock
Alternating Timed Automata (1-ATA) and its natural subclasses. A notion of
1-ATA with loop-free-resets is defined. This automaton class is shown to be
expressively equivalent to the temporal logic $\regmtl$ which is
$\mathsf{MTL[F_I]}$ extended with a regular expression guarded modality.
Moreover, a subclass of future timed MSO with k-variable-connectivity property
is introduced as logic $\qkmso$. In a Kamp-like result, it is shown that
$\regmtl$ is expressively equivalent to $\qkmso$. As our second result, we
define a notion of conjunctive-disjunctive 1-clock ATA ($\wf$ 1-ATA). We show
that $\wf$ 1-ATA with loop-free-resets are expressively equivalent to the
sublogic $\F\regmtl$ of $\regmtl$. Moreover $\F\regmtl$ is expressively
equivalent to $\qtwomso$, the two-variable connected fragment of $\qkmso$. The
full class of 1-ATA is shown to be expressively equivalent to $\regmtl$
extended with fixed point operators.
