Rotational spectra of weakly bound complexes of chlorofluoromethane (CH2ClF) and difluoromethane (CH2F2) with propyne (HCCCH3) have been measured using chirped-pulse and resonant-cavity Fourier-transform microwave spectroscopy, adding to a relatively small body of high resolution spectroscopic data on propyne complexes. Both dimers contain CH/pi contacts, as well as secondary contacts between one or both halogen atoms and the methyl group of propyne. A detailed structural determination for CH2F2 center dot center dot center dot propyne has been made by study of the normal, one deuterated and four C-13 substituted isotopologues, with the second lowest energy configuration predicted from ab initio calculations agreeing well with the observed structure. Experimental rotational constants for the most abundant isotopologue of CH2F2 center dot center dot center dot propyne are A(00) = 5815.5858(15) MHz, B-00 = 1341.1191(S) MHz, C-00 = 1099.2040(4) MHz (uncorrected for internal rotation effects), and the dipole moment components, determined by Stark effect measurements, are mu(a) = 1.568(2) D, mu(b) = 0.587(2) D, and mu(tot) = 1.674(3) D. For CH2ClF center dot center dot center dot propyne, only Cl-33 and Cl-37 isotopologues have been assigned, providing rotational constants and chlorine atom coordinates consistent with the lowest energy structure from a series of ab initio predictions. Rotational constants for the Cl-35 isotopologue are A = 3423.639(7) MHz, B = 1253.7562(20) MHz, and C = 1200.4828(15) MHz and the diagonal and two off diagonal components of the quadrupole coupling tensor have also been determined.