  The Cosmic Axion Spin Precession Experiment (CASPEr) is a nuclear magnetic
resonance experiment (NMR) seeking to detect axion and axion-like particles
which could make up the dark matter present in the universe. We review the
predicted couplings of axions and axion-like particles with baryonic matter
that enable their detection via NMR. We then describe two measurement schemes
being implemented in CASPEr. The first method, presented in the original CASPEr
proposal, consists of a resonant search via continuous-wave NMR spectroscopy.
This method offers the highest sensitivity for frequencies ranging from a few
Hz to hundreds of MHz, corresponding to masses $ m_{\rm a} \sim
10^{-14}$--$10^{-6}$ eV. Sub-Hz frequencies are typically difficult to probe
with NMR due to the diminishing sensitivity of magnetometers in this region. To
circumvent this limitation, we suggest new detection and data processing
modalities. We describe a non-resonant frequency-modulation detection scheme,
enabling searches from mHz to Hz frequencies ($m_{\rm a} \sim
10^{-17}$--$10^{-14} $ eV), extending the detection bandwidth by three decades.
