Cereal quality usually declines through moisture, air, heat, odours or pests. Storage cannot make an unsafe or contaminated product acceptable.
Keep it cool and dry
A closed cupboard away from the stove, kettle and direct sunlight is usually better than an open shelf near humidity.
Use the inner bag well
Roll or clip the original liner after each use. An airtight container can add protection, but keep the package label or record the product and date for allergen and recall information.
Rotate packages
Finish the oldest open package first. Avoid opening several similar cereals at once unless your household will use them promptly.
Know when to discard
Discard cereal with insects, mould, unusual moisture, rancid odour or contamination. A stale texture alone is a quality issue, but uncertainty about safety should favour disposal and local food-safety advice.