Conformations of cationic polyelectrolytes (PEs), a weak poly(2-vinylpyridine) (P2VP) and a strong poly(N-methyl-2-vinylpyridinium iodide) (qP2VP), adsorbed on mica from saline solutions in the presence of counterions of different valences are studied using in situ atomic force microscopy (AFM). Quantitative characteristics of chain conformations are analyzed using AFM images of the adsorbed molecules. The results of the statistical analysis of the chain contour reveal collapse of the PE coils when ionic strength is in a range from tens to hundreds of millimoles per kilogram and reexpansion of the coils with a further increase of ionic strength up to a region of the saturated saline solutions. The competition between monovalent and multivalent counterions simultaneously present in solutions strongly affects conformations of PE chains even at a very small fraction of multivalent counterions. Shrinkage of PE coils is steeper for multivalent counterions than for monovalent counterions. However, the re-expansion is only incremental in the presence of multivalent counterions. Extended adsorbed coils at low salt concentrations and at very high concentrations of monovalent salt exhibit conformation corresponding to a 2D coil with 0.95 fraction of bound segments (segments in "trains") in the regime of diluted surface concentration of the PE. Shrunken coils in the intermediate range of ionic strength resemble 3D-globules with 0.8 fraction of trains. The incrementally re-expanded PE coils at a high ionic strength remain unchanged at higher multivalent salt concentrations up to the solubility limit of the salt. The formation of a strong PE complex with multivalent counterions at high ionic strength is not well understood yet. A speculative explanation of the observed experimental result is based on possible stabilization of the complex clue to hydrophobic interactions of the backbone.