Results are reported for the conductance anisotropies in single crystals of the layered colossal magnetoresistive manganites. Well below the magnetic ordering temperatures, the zero-field anisotropy increases from similar to 230 for La1.24Sr1.76Mn2O7 to >10000 for La1.4Sr1.6Mn2O7, consistent with a c-axis antiferromagnetic ground state in the latter, while the spin-independent conductivity anisotropy only increases from similar to 230 to similar to 300. Significant c-axis ferromagnetic fluctuations are seen in La1.4Sr1.6Mn2O7, but no evidence is found for the recently reported two-dimensional magnetic ordering transition at higher temperatures. Direct evidence suggests that spin-orbit coupling is weaker than any other possible sources of orbital ordering. [S0163-1829(99)11613-8].