  We construct Coleff-Herrera products and Bochner-Martinelli type residue
currents associated with a tuple $f$ of weakly holomorphic functions, and show
that these currents satisfy basic properties from the (strongly) holomorphic
case, as the transformation law, the Poincar\'e-Lelong formula and the
equivalence of the Coleff-Herrera product and the Bochner-Martinelli type
residue current associated with $f$ when $f$ defines a complete intersection.
