Deformations of nilpotent parts of the Neveu-Schwarz superalgebra and of the Ramond superalgebra are studied herein. This study consists of the computation of the second cohomology space with coefficients in the adjoint representation by means of spectral sequences, the explicit construction of infinitesimal deformations, the extension of these infinitesimal deformations to one-parameter deformations, the realization of these deformations, and the construction of multiparameter deformations.