  We study in detail the dynamics of unstable two-level quantum systems by
adopting the Bloch-sphere formalism of qubits. By employing the Bloch-vector
representation for such unstable qubit systems, we identify a novel class of
critical scenarios in which the so-called energy-level and decay-width vectors,
${\bf E}$ and ${\bf\Gamma}$, are orthogonal to one another, and the parameter
$r = |{\bf \Gamma}|/(2|{\bf E}|)$ is less than 1. Most remarkably, we find that
critical unstable qubit systems exhibit atypical behaviours like
coherence--decoherence oscillations when analysed in an appropriately defined
co-decaying frame of the system. In the same frame, a unit Bloch vector ${\bf
b}$ describing a pure critical qubit will sweep out unequal areas during equal
intervals of time, while rotating about the vector ${\bf E}$. These phenomena
emerge beyond the usual oscillatory pattern due to the energy-level difference
of the two-level quantum system. Interestingly enough, we observe that these
new features will persist even for quasi-critical scenarios, in which the
vectors ${\bf E}$ and ${\bf\Gamma}$ are not perfectly orthogonal to each other.
Applications of our results to quantum information and to unstable
meson--antimeson and other systems are discussed.
