The Fortran 77 codes BiM and BiMD are based on blended implicit methods, namely a class of L-stable Block Implicit Methods providing a (relatively) easy definition of suitable nonlinear splittings for solving the corresponding discrete problems, [41,43,46,54]. In particular: the code BiM (release 2.0, April 2005) implements a variable order-variable stepsize method for (stiff) initial value problems for ODEs. The order of the method varies from 4 to 12, according to a suitable order variation strategy. All the details concerning the strategies implemented in the code BiM are described in [47,48,53] (see also Cecilia Magherini’s PhD thesis, also available as a compressed file); the code BiMD (release 1.1.2, November 2014) is a generalization of the code BiM for solving (stiff) initial value problems for linearly implicit DAEs of index up to 3 with constant mass matrix [54], namely problems in the form M y’ = f(t,y), where M is a constant, possibly singular, matrix.