The research in the present paper was motivated by the conjecture of Ryjáček that every locally connected graph is weakly pancyclic. We show that the conjecture holds for several classes of graphs. In particular, for a connected, locally connected graph G of order at least 3 , our results are as follows: If G is ( K 1 + ( K 1 ∪ K 2 ) ) -free, then G is weakly pancyclic. If G is ( K 1 + ( K 1 ∪ K 2 ) ) -free, then G is fully cycle extendable if and only if 2 δ ( G ) ≥ n ( G ) . If G is { K 1 + K 1 + K ̄ 3 , K 1 + P 4 } -free or { K 1 + K 1 + K ̄ 3 , K 1 + ( K 1 ∪ P 3 ) } -free, then G is fully cycle extendable. If G is distinct from K 1 + K 1 + K ̄ 3 and { K 1 + P 4 , K 1 , 4 , K 2 + ( K 1 ∪ K 2 ) } -free, then G is fully cycle extendable. Furthermore, we prove that a degree condition weaker than locally Dirac or locally Ore guarantees fully cycle extendability.