  It has been suggested that relic long-lived strongly interacting massive
particles (SIMPs, or $X$ particles) existed in the early universe. We study
effects of such long-lived unstable SIMPs on big bang nucleosynthesis (BBN)
assuming that such particles existed during the BBN epoch, but then decayed
long before they could be detected. The interaction strength between an $X$
particle and a nucleon is assumed to be similar to that between nucleons. We
then calculate BBN in the presence of the unstable neutral charged $X^0$
particles taking into account the capture of $X^0$ particles by nuclei to form
$X$-nuclei. We also study the nuclear reactions and beta decays of $X$-nuclei.
We find that SIMPs form bound states with normal nuclei during a relatively
early epoch of BBN. This leads to the production of heavy elements which remain
attached to them. Constraints on the abundance of $X^0$ particles during BBN
are derived from observationally inferred limits on the primordial light
element abundances. Particle models which predict long-lived colored particles
with lifetimes longer than $\sim$ 200 s are rejected based upon these
constraints.
