  We prove a version of Clifford's theorem for metrized complexes. Namely, a
metrized complex that carries a divisor of degree $2r$ and rank $r$ (for
$0<r<g-1$) also carries a divisor of degree $2$ and rank $1$. We provide a
structure theorem for hyperelliptic metrized complexes, and use it to classify
divisors of degree bounded by the genus. We discuss a tropical version of
Martens' theorem for metric graphs.
