Morpholinos (MOs) are DNA analogues whose uncharged nature can bring fundamental advantages to surface hybridization technologies such as DNA microarrays, by using MOs as the immobilized, or "probe", species. Advancement of MO-based diagnostics, however, is challenged by limited understanding of the surface organization of MO molecules and of how this organization impacts hybridization kinetics and thermodynamics. The present study focuses on hybridization kinetics between monolayers of MO probes and DNA targets as a function of the instantaneous extent of hybridization (i.e., duplex coverage), total probe coverage, and ionic strength. Intriguingly, these experiments reveal distinct kinetic stages, none of which are consistent with Langmuir kinetics. The initial stage, in which duplex coverage remains relatively sparse, indicates confluence of two effects: blockage of target access to unhybridized probes by previously formed duplexes and deactivation of the solid support due to consumption of probe molecules. This interpretation is consistent with a surface organization in which unhybridized MO probes localize near the solid support, underneath a layer of MO-DNA duplexes. As duplex coverage builds, provided saturation is not reached first, the initial stage can transition to an unusual regime characterized by near independence of hybridization rate on duplex coverage, followed by a prolonged approach to equilibrium. The possible origins of these more complex latter behaviors are discussed. Comparison with published data for DNA and peptide nucleic acid (PNA) probes is carried out to look for universal trends in kinetics. This comparison reveals qualitative similarities when comparable surface organization of probes is expected. In addition, MO monolayers are found capable of a broad range of reactivities that span reported values for PNA and DNA probes.