The invention relates to non-crosslinked non-polypeptide polymers containing biodegradable lipophilic side chains incorporating methylene diester units of the formula --[--CO--O--C(R.sup.1 R.sup.2)--O--CO--]--, where R.sup.1 and R.sup.2 each represents a hydrogen atom or a carbon-attached monovalent organic group or R.sup.1 and R.sup.2 together form a carbon-attached divalent organic group. The lipophilic moieties are biodegradatively cleavable to yield a water-soluble polymer.