The　minimal　energy　of　unicyclic　Hückel　molecular　graphs　with　Kekulé　structures,　i.e.,　unicyclic　graphs　with　perfect　matchings,　of　which　all　vertices　have　degrees　less　than　four　in　graph　theory,　is　investigated.　The　set　of　these　graphs　is　denoted　by　Hnl　such　that　for　any　graph　in　Hnl,　n　is　the　number　of　vertices　of　the　graph　and　l　the　number　of　vertices　of　the　cycle　contained　in　the　graph.　For　a　given　n(n　≥　6),　the　graphs　with　minimal　energy　of　Hnl　have　been　discussed.　©　2005　Springer　Science+Business　Media,　Inc.