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It is now well known that non-local observables in critical statisticallattice models, polymers and percolation for example, may be modelled in thecontinuum scaling limit by logarithmic conformal field theories. Fusion rulesfor such theories, sometimes referred to as logarithmic minimal models, havebeen intensively studied over the last ten years in order to explore therepresentation-theoretic structures relevant to non-local observables.Motivated by recent lattice conjectures, this work studies the fusion rules ofthe $N=1$ supersymmetric analogues of these logarithmic minimal models in theNeveu-Schwarz sector. Fusion rules involving Ramond representations will beaddressed in a sequel.

Fusion rules for the logarithmic $N=1$ superconformal minimal models I: the Neveu-Schwarz sector