Dipeptidyl peptidase IV (DPP-IV)-inhibiting compounds are provided that have formula I: wherein n is 1 to 3; X is CH2; S; O; CF2 or C(CH3)2; Z is H; halogen; hydroxyl; (C1-6)alkoxy; (C1-12)alkyl; (C3-12)cycloalkyl; phenyl; or heteroaryl; where the phenyl and heteroaryl groups are optionally mono- or independently plurisubstituted with R7; optionally, X together with an adjacent ring carbon and Z form a fused cyclopropyl; and optionally, one of the bonds in the ring containing X is a double bond; and CriRii, R1, R1, R3, R4 and R5 are as described herein. Methods for preparing these compounds, and methods for treating diabetes, especially Type II diabetes, and other related diseases are described using the compounds of formula I in pharmaceutical compositions which contain these compounds. Pharmaceutical compositions which contain combinations of these compounds with other antidiabetic agents are also described herein.