We Initiate a Study of Harmonic Functions on Hypergroups.In Particular, We Introduce the Concept of a Nilpotent Hypergroup and Show Suchhypergroup Admits an Invariant Measure As Well As a Liouville Theorem Forbounded Harmonic Functions. Further, Positive Harmonic Functions on Nilpotenthypergroups Are Shown to Be Integrals of Exponential Functions. For Arbitraryhypergroups, We Derive a Harnack Inequality For Positive Harmonic Functions Andprove a Liouville Theorem For Compact Hypergroups. We Discuss an Application Toharmonic Spherical Functions.