SQL order by two columns & loop

+----------+---------+

| Category | id      |

+----------+---------+
| 1        | 70      |

| 1        | 71      |

| 3        | 80      |

| 4        | 73      |

| 5        | 83      |

| 5        | 81      |

| 5        | 69      |

| 4        | 72      |

| 1        | 74      |

| 4        | 82      |

| 3        | 85      |

| 3        | 68      |

| 4        | 88      |

| 6        | 66      |

+----------+---------+

I have the following table, and need a way of producing results which will involve an SQL statement with a loop, but i'm not sure how.

First I want to take out the results in order of category, so 1, 3, 4, 5, 6, and for each of those categories, order the records by id, (category/id  1/70, 1/71, 1/74, 3/68, 3/80, 3/85, 4/72, 4/73, 4/88 etc...).

When there are no more records to show, I want to loop back to the first smallest category and ID number.

How is this possible? Note that the categories do not ascend by +1 every time, so it is not possible to take the previous category number and +1.

Thanks in advance.

Izzy