One goal of algebraic coding theory is to find linear error-correcting codes with maximum error-correcting capacity.  Correlated to the error-correcting capacity of a code C are the generalized Hamming weights of C.  Thus, using Hochster's formula and techniques of commutative algebra, we will derive the generalized Hamming weights for one class of BCH codes and partially extend these results to special cases of another class of BCH codes.